U.S. patent number 5,200,816 [Application Number 07/734,310] was granted by the patent office on 1993-04-06 for method and apparatus for color processing with neural networks.
This patent grant is currently assigned to Scitex Corporation Ltd.. Invention is credited to Oded M. Rose.
United States Patent |
5,200,816 |
Rose |
April 6, 1993 |
Method and apparatus for color processing with neural networks
Abstract
A method and apparatus for constructing, training and utilizing
an artificial neural network (also termed herein a "neural
network", an ANN, or an NN) in order to transform a first color
value in a first color coordinate system into a second color value
in a second color coordinate system.
Inventors: |
Rose; Oded M. (Herzliya,
IL) |
Assignee: |
Scitex Corporation Ltd.
(Herzliya, IL)
|
Family
ID: |
11062578 |
Appl.
No.: |
07/734,310 |
Filed: |
July 19, 1991 |
Foreign Application Priority Data
Current U.S.
Class: |
358/518; 706/17;
706/31 |
Current CPC
Class: |
H04N
1/6019 (20130101); H04N 1/6033 (20130101) |
Current International
Class: |
H04N
1/60 (20060101); H04N 001/40 () |
Field of
Search: |
;358/75-80,433 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
|
|
|
|
|
|
|
0144188A2 |
|
Dec 1985 |
|
EP |
|
2214987 |
|
Aug 1990 |
|
JP |
|
2215277 |
|
Aug 1990 |
|
JP |
|
2216971 |
|
Aug 1990 |
|
JP |
|
2231760A |
|
Nov 1990 |
|
GB |
|
Other References
"Application of Neural Networks to Computer Recipe Prediction",
Color Research & Application, Feb. 1991, 16(1). (Bishop et al).
.
R. K. Molla, "Electronic Color Separation", R. K. Printing &
Publishing, New York, 1988. .
G. Wyszecki et al. "Color Science", Wiley & Sons, 1982. .
Rumelhart et al, "Parallel Distributed Processing", MIT Press,
1986. .
J. Stoer, "Introduction to Numerical Analysis", Spring-Verlag, New
York, 1980, chapter 2. .
Marquet M., "Dehalftoning of Negatives by Optical Filtering",
Optica Acta 6, pp. 404-405, 1959. .
M. Stone et al, "Color Gamut Mapping and the Printing of Digital
Color Images", ACM Trans. on Graphics, 7(4), Oct. 1988, pp.
249-292. .
Wasserman P. D., "Neural Computing Theory and Practice", Van
Nostrand Reinhold, New York, 1989, pp. 43-59. .
Anderson, J. A. et al, "Neurocomputing", MIT Press, 1988. .
Marquet M. et al, "Interpretation of Particular Aspects of
Dehalftoned Images", Optica Acta 8, pp. 267-277, 1961. .
Kermisch D. et al, "Fourier Spectra of Halftone Screens", J. Opt.
Soc. Amer., 65, pp. 716-723, 1975. .
P. G. Engeldrum, "Almost Color Mixture Functions", Jou. of Imaging
Technology, 14(4), Aug., 1988. .
M. Wright, "Neural Networks Tackle Real-World Problems", Technology
Update, EDN, Nov. 8, 1990. .
IT8.7/2, "Color Reflection Target for Input Scanner Calibration",
Graphic Arts Perpress, Draft 1, May 13, 1991..
|
Primary Examiner: Brinich; Stephen
Attorney, Agent or Firm: Ladas & Parry
Claims
I claim:
1. A method for providing a neural network including the steps
of:
providing a neural network structure including a plurality of
neurons for receiving a first color value from among a first set of
color values which first color value is to be transformed into a
corresponding second color value from among a second set of color
values and for providing an output indication of the corresponding
second color value; and
training the neural network structure on a plurality of ordered
pairs, each ordered pair comprising a first color value from among
the first set of color values and a corresponding second color
value from among the second set of color values.
2. A method according to claim 1 wherein one or both of the
plurality of first color values and the plurality of second color
values is a systematic representation of the respectively
corresponding one of the first and second sets of color values.
3. A method according to claim 2 wherein one of the first and
second sets of color values is defined within a color coordinate
system and wherein each region of a predetermined size within the
order coordinate system is represented by at least one color value
within the plurality of color values corresponding to the set of
color values defined within the color coordinate system.
4. A method according to claim 2 wherein one of the first and
second sets of color values is defined within a color coordinate
system which may be partitioned into regions and wherein each
region within the partition is represented by at least one color
value within the plurality of color values corresponding to the set
of color values defined within the color coordinate system.
5. A method according to claim 1 and wherein said first set of
color values is identical to the second set of color values.
6. A method according to claim 1 and wherein each second color
value, represented in visual form, is substantially identical in
appearance to the corresponding first color value, represented in
visual form.
7. A method according to claim 1 and wherein said plurality of
neurons comprises:
an input layer of neurons comprising at least one input neuron;
at least one hidden layer of neurons each comprising at least one
hidden neuron; and
an output layer of neurons comprising at least one output
neuron.
8. A method according to claim 7 wherein the first color value is
also to be transformed into a corresponding third color value from
among a third set of color values, the neural network structure is
operative to provide an output indication of the corresponding
second and third color values, the output layer of neurons
comprises at least a first plurality of output neurons
corresponding to the dimension of the second color value and a
second plurality of output neurons corresponding to the dimension
of a third color value and each ordered pair comprises a first
color value and a corresponding concatenation of a second color
value and a third color value.
9. A method according to claim 8 wherein the appearance of the
second color value, when represented using a predetermined first
color output device, is similar to the appearance of the third
color value, when represented using a predetermined second color
output device.
10. A method according to claim 7 wherein each neuron in the at
least one hidden layer and in the output layer comprises summing
means for computing a weighted sum of a plurality of inputs.
11. A method according to claim 7 wherein each neuron in the at
least one hidden layer and in the output layer also comprises means
for computing a nonlinear function of the output of said summing
means.
12. A method according to claim 11 and wherein the nonlinear
functions corresponding to substantially all of the neurons in the
at least one hidden layer and in the output layer are equal.
13. A method according to claim 1 wherein said neural network
structure is a feed-forward network structure.
14. A method according to claim 1 wherein each ordered pair is
characterized in that there is a predetermined relationship between
the second color value and the corresponding first color value.
15. A method according to claim 4 wherein the plurality of regions
comprises regions of non-equal size.
16. A method according to claim 4 wherein the plurality of regions
comprises regions of equal size.
17. A method according to claim 1 and also comprising the step of
subsequently employing the neural network for transforming a first
color value from the first plurality of color values into a second
color value from the second plurality of color values.
18. A method according to claim 17 and also comprising the step of
employing the second color value obtained by transforming the first
color value in order to control operation of a color processing
system to be calibrated.
19. A method according to claim 1 wherein at least one interneuron
connection is defined between a pair of neurons from among the
plurality of neurons in the neural network and wherein said step of
training comprises the steps of:
providing the first color value of an individual ordered pair to
the neural network;
back-propagating an error value indicative of the difference
between the second color value of said individual ordered pair and
the output of the neural network for the first color value; and
modifying at least one of the at least one interneuron
connections.
20. A method according to claim 19 wherein each of the at least one
interneuron connections defines a weight associated therewith and
said step of modifying comprises the step of changing the value of
the weight.
21. Apparatus for providing a neural network including:
a neural network structure including a plurality of neurons for
receiving a first color value from among a first set of color
values which first color value is to be transformed into a
corresponding second color value from among a second set of color
values and for providing an output indication of the corresponding
second color value; and
means for training the neural network structure on a plurality of
ordered pairs, each ordered pair comprising a first color value
from among the first set of color values and a corresponding second
color value from among the second set of color values.
22. Apparatus according to claim 21 wherein one or both of the
plurality of first values and the plurality of second color values
is a systematic representation of the respectively corresponding
one of the first and second sets of color values.
23. A neural network comprising:
a trained neural network structure including a plurality of neurons
for receiving a first color value from among a first set of color
values which first color value is to be transformed into a
corresponding second color value from among a second set of color
values and for providing an output indication of the corresponding
second color value.
24. A neural network according to claim 23 wherein the trained
neural network structure was trained on a plurality of ordered
pairs, each ordered pair comprising a first color value from among
the first set of color values and a corresponding second color
value from among the second set of color values, one or both of the
plurality of first color values and the plurality of second color
values being a systematic representation of the respective
corresponding one of the first and second sets of color values.
25. A neural network according to claim 23 wherein the second color
value includes a black component and the neural network structure
is characterized in that at least some of the color content of the
first color value is transformed to the black component of the
second color value.
26. A method for transforming a first color value from among a
first set of color values into a second color value from among a
second set of color values, the method comprising the steps of:
providing a trained neural network structure including a plurality
of neurons for receiving a first color value from among the first
set of color values which first color value is to be transformed
into a corresponding second color value from among the second set
of color values and for providing an output indication of the
corresponding second color value; and
employing the trained neural network structure in order to
transform a first color value from among the first set of color
values into a second color value from among the second set of color
values.
27. A method according to claim 26 wherein the trained neural
network structure was trained on a plurality of ordered pairs, each
ordered pair comprising a first color value from among the first
set of color values and a corresponding second color value from
among the second set of color values, one or both of the plurality
of first values and the plurality of second color values being a
systematic representation of the respective corresponding one of
the first and second sets of color values.
28. A method according to claim 26 and also comprising the step of
controlling operation of a color processing system to be calibrated
using the second color value obtained in said employing step.
29. A method according to claim 28 wherein said step of controlling
comprises the step of using said color writing device to create
upon a second substrate a duplicate of an analog representation of
a color image upon a first substrate.
30. A method according to claim 28 wherein said step of controlling
comprises the step of using said color processing system to create
an input copy of a color image which, when processed by said
calibrated system, will result in a given output copy of said color
image.
31. A method according to claim 28 wherein said color processing
system to be calibrated comprises a color reading device operative
to convert an analog representation of a color image into a digital
representation thereof.
32. A method according to claim 28 wherein said color processing
system to be calibrated comprises a color writing device operative
to convert a digital representation of a color image into an analog
representation thereof.
33. A method according to claim 32 wherein said color writing
device comprises a color monitor display.
34. A method for constructing a look-up table relating a first
multiplicity of values to a second multiplicity of values
comprising the steps of:
providing an artificial neural network relating the first
multiplicity of values to the second multiplicity of values;
providing a plurality of look-up table addresses;
operating the artificial neural network on the plurality of look-up
table addresses, thereby to obtain a plurality of processed look-up
table addresses; and
storing the plurality of processed look-up table addresses as the
contents of the look-up table.
35. A method according to claim 34 wherein the first and second
multiplicities of values respectively comprise first and second
multiplicities of color values.
36. A method according to claim 34 wherein the step of providing an
artifical neural network comprises the steps of:
providing artificial neural network training data representing the
first and second multiplicity of values; and
employing the artifical neural network training data to train an
artifical neural network.
37. Apparatus for constructing a look-up table relating a first
multiplicity of values to a second multiplicity of values
comprising:
an artifical neural network relating the first multiplicity of
values to the second multiplicity of values;
means for operating the artificial neural network on a plurality of
look-up table addresses, thereby to obtain a plurality of processed
look-up table addresses; and
means for storing the plurality of processed look-up table
addresses as the contents of the look-up table.
38. Digital storage apparatus comprising:
a representation of a look-up table relating a first multiplicity
of values to a second multiplicity of values, the look-up table
having been constructed by the following method:
providing an artificial neural network relating the first
multiplicity of values to the second multiplicity of values;
providing a plurality of look-up table addresses;
operating the artificial neural network on the plurality of look-up
table addresses, thereby to obtain a plurality of processed look-up
table addresses; and
storing the plurality of processed look-up table addresses as the
contents of the look-up table.
39. A method for constructing apparatus for sampling the color
processing characteristics of a color processing device, said color
processing device being operative to convert a first representation
of a color image into a second representation thereof,
the method comprising the step of repeating at least once the steps
of:
providing first and second representations of a color image, said
representations respectively comprising a first multiplicity of
first color values and a second multiplicity of second color values
corresponding thereto, said first and second representations being
characterized in that processing said first representation with
said color processing device defines said second
representation;
providing an artificial neural network which, when operated on each
individual one of the second multiplicity of second color values,
gives a value substantially equal to the corresponding one of said
first multiplicity of first color values; and
operating the artifical neural network on the first representation
of the color image, thereby to provide a third representation
thereof.
40. A system for constructing apparatus for sampling the color
processing characteristics of a color processing device, said color
processing device being operative to convert a first representation
of a color image to a second representation thereof, the system
comprising:
means for providing first and second representations of a color
image, said representations respectively comprising a first
multiplicity of first color values and a second multiplicity of
second color values corresponding thereto, said first and second
representations being characterized in that processing said first
representations with said color processing device defines said
second representation;
an artificial neural network which, when operated on each
individual one of the second multiplicity of second color values,
gives a value substantially equal to the corresponding one of said
first multiplicity of first color values; and
means for operating the artifical neural network on the first
representation of the color image, thereby to provide a third
representation thereof.
Description
FIELD OF THE INVENTION
The present invention relates to artificial neural networks
generally and to techniques for tone and color reproduction control
in graphic arts generally.
BACKGROUND OF THE INVENTION
Neural networks, or artificial neural networks, are a branch of
study related to the discipline of artificial intelligence. A
neural network "learns" a set of training data and subsequently can
use the "experience" it has acquired by learning the training data
to process other data. It is now being realized that neural
networks have applications in practical problems outside the
research laboratory.
UK Published Patent Application No. 2231760A (Application No.
9009467.3) to Apple Computer Inc. discusses use of a neural network
for processing RGB signals, in order to assist in selecting color
combinations. The associative memory system disclosed is said to
have particular application in the design of color interfaces for
computer systems based on user preferences.
Japanese patents 90-215277,90-216971 and 90-214987, all to
Matsushita Electric Industries Co. Ltd., seem to disclose uses of
neural networks for color image processing.
A British journal article published February, 1991 in Color
Research and Application, 16(1) and entitled "Application of neural
networks to computer recipe prediction" discusses uses of neural
networks for computerized prediction of color recipes. The article
teaches that the use of neural networks offers several potential
advantages including that it is not necessary to prepare a special
database in order to use the neural network method.
Scanning methods are reviewed in R. K. Molla, Electronic Color
Separation, R. K. Printing & Publishing, New York, 1988, the
disclosure of which is incorporated herein by reference. The
principles of color are explained in G. Wyszecki and W. S. Stiles,
Color Science, Wiley & Sons, 1982, the disclosure of which is
incorporated herein by reference.
Generally speaking, tone and color reproduction control in high
quality graphic arts reproduction is still far from a science. This
is particularly evident when a given acceptable result, already
realized using given reproduction apparatus, is sought to be
realized using other apparatus or using the same apparatus but with
a different setting, such as a GCR setting relative to a normal
"key black" setting. In such cases, a high degree of expertise,
combined with time, effort, expense and patience is required to
calibrate the additional apparatus. The results are not always
satisfactory.
Unidimensional calibrations in graphic arts, in which a plurality
of calibrations are carried out, each being a function of only one
color, are known. State of the art techniques include gray balance
correction and plotter output calibration techniques. Another
example of unidimensional calibration is the automatic TCR (tone
and color reproduction) correction process disclosed in published
European Application 84307997.1 of Xerox Corporation (Publication
number 0144188 A2).
The disadvantage of unidimensional calibrations is that they are
only accurate in certain portions of the color space, since a full
determination of color is multidimensional, typically having three
or four components. For example, the teaching of the
above-mentioned published European Application 8437997.1 is
relatively inaccurate except in the area of a particular machine's
primary color coordinate axes. Gray balance techniques are
relatively inaccurate except for a relatively small volume of the
color space, comprising gray colors only. Also, the apparatus
disclosed in the above-cited published European Application
8437997.1 can be calibrated only by its own output.
Methods of computing a multidimensional function to fit a given set
of vectors are known. Interpolative methods may be used if the data
is suitably distributed. However the desired conditions regarding
the distribution do not always hold in color processing
applications, because the data is often not produced directly but
rather is the end result of certain procedures (such as scanning,
printing, etc.) which are performed on initial preselected
data.
In color image processing, there are a number of applications, such
as gamut mapping, in which it is desired to compare a first color
coordinate system to a second color coordinate system.
Gamut mapping is discussed in the following article: Stone, Maureen
et al, "Color Gamut Mapping and the Printing of Digital Color
images", ACT Transactions on Graphics 7(4), October 1988, pp.
249-292.
U.S. Pat. No. 4,500,919 to Schreiber discloses a LUT system for
producing color reproductions of an image in which an operator may
interactively manipulate a display of the scanned image in order to
introduce aesthetic, psychophysically referenced corrections
therein. Schreiber teaches that it is desirable for such a system
to provide automatic compensation for the effects of ink and paper
while allowing the operator to input aesthetic alterations.
U.S. Pat. No. 4,719,954 to Fujita et al. describes a method and
apparatus for creating a color conversion table between scanned
colors of a color chart, typically in the Red-Green-Blue (RGB)
color coordinate system, and printable colors, typically in the
Cyan-Magenta-Yellow-Black (CMYK) color coordinate system, and for
using the color conversion table to reproduce a selected measured
color in a color specimen. If the selected measured color does not
coincide with a value in the color conversion table, an
interpolation step is performed.
The method of Fujita et al also includes a correction step when
reproduction is performed under different printing conditions. The
correction step compensates for the difference between the two
printing conditions.
Image creation systems typically comprise a computer with
associated graphic software for generating digital representations
of color images and/or modifying digital representations of color
images, and a plotter or other color output device for transforming
the digital representations into analog representations. The analog
representation may be created on any suitable substrate, such as on
a dia. If desired, e.g. in pre-press applications, the resulting
dia can be scanned.
Examples of commercially available graphic software are Photoshop,
by Adobe Systems Inc., Mountainview, Calif., USA, usable in
conjunction with the Mac II by Apple Computer Inc., USA; and PC
Paintbrush Plus, by ZSoft, San Francisco, Calif., USA, usable in
conjunction with the IMB PC. Examples of commercially available
color printer are 4cast, by DuPont, Wilmington, Del., USA, and the
LVT Model 1620 digital image recorder by Light Valve Technology,
Rochester, N.Y., USA.
SUMMARY OF THE INVENTION
The following terms as used in the present specification and claims
should be construed in the following manner:
Analog representation of a color image: A representation of a color
image which is perceivable by the human eye as a color image. The
representation may appear upon a transparency, a photograph, a CRT
display, a printed page, etc.
Digital representation of a color image: Any representation of a
color image which is expressed in discrete symbols, such as
numerical symbols. A common digital representation of a color image
is a digital file comprising a plurality of numerical values
corresponding to a plurality of pixels into which the color image
has been divided, each such numerical value representing some
aspect pertaining to the color appearance of the corresponding
pixel.
Substrate: Physical apparatus bearing or displaying an analog
representation of an image, e.g. transparency, Cromalin (registered
trademark), CRT display, photograph, paper, surfaces suitable for
painting on, etc.
Range of color processing apparatus: The totality of color values
which can be output by the color processing apparatus.
Domain of color processing apparatus: The totality of color values
which can be input by the color processing apparatus.
Color processing apparatus: Apparatus which inputs a first
representation of a color image (digital or analog) and converts it
into a second representation of a color image (digital or analog),
thereby to define a transformation from at least a portion of the
range of the color processing apparatus into the domain.
Image creation system: Apparatus which creates an image internally
or one which takes as input a representation of a color image and
modifies it. Such a system can create the color image from
geometrical shapes, can alter the shape and can select and/or
modify the color of the color image.
Color reading apparatus: Apparatus which inputs an analog
representation of a color image and converts it to a digital
representation thereof. e.g., ECSS, DECSS, colorimeters, spectrum
analyzers, densitometers. Typically, the digital representation is
expressed in a coordinate system such as XYZ, CMYK, RGB, etc.
Color output device; printing, machine/device/system; output
apparatus, recording apparatus, color writing device, etc.: Any
apparatus which inputs a digital representation of a color image
and converts it into an analog representation thereof. For example:
conventional, offset, gravure, or other printing apparatus
employing inks, conventional or direct digital proofing machines,
plotters or color recorders which expose photographic materials,
electrostatic printing systems employing powder colorants, color
monitors, and color CRT displays.
Calibration: Adjusting color processing apparatus in order to
obtain representations, having predetermined substantially
objective color characteristics, of color images sought to be
processed.
Color value: A representation of a color, typically in a color
coordinate system such as but not limited to RGB, L*a*b*, XYZ
coordinate systems and device dependent coordinate systems such as
color head signals e.g. RGB, ink percentages e.g. CMYK, etc.
Colorant, ink, etc.: Any stimulant of the human eye's light energy
receptors, typically through emission, transmission or reflection
of photons, including liquid colorants, powder colorants,
photographic colorants, phosphors, etc.
Colorant values: A digital representation of the amount of a
colorant which it is sought to use.
Color coordinate system: A coordinate system in which color values
are defined, including but not limited to RGB, CMY, CMYK, LHS, LAB,
XYZ and 7 dimensional color coordinate systems. In some coordinate
systems, particularly coordinate systems having more than three
dimensions, a single color, as perceived by the human eye, may be
represented in more than one way.
The term "color coordinate system" is intended to include color
spaces.
A variety of color spaces are discussed in the above-referenced
volume by Wyszecki and Stiles.
It is appreciated that any references to color, color images, color
values, colorant values, etc. in the present specification are
intended to include the instances of black and white as colors or
color values, black and white images, black colorant and black ink.
The following abbreviations are used:
TCR: tone and color reproduction
GCR: gray component replacement
UCR: Undercolor removal
UCA: Undercolor addition
RGB: red, green, blue. More generally, the term as used herein may
refer to any color signals produced by a color reading device. In a
color separation scanner, the term normally refers to the color
separation signals of the scanner prior to processing thereof.
CMYK: cyan, magenta, yellow, black (colorants such as inks). More
generally, the term as used herein refers to any signals which may
serve as input for a color printing device.
ECSS: electronic color separation scanner
DECSS: digital electronic color separation scanner
The present invention seeks to provide a method and apparatus for
constructing, training and utilizing an artificial neural network
(also termed herein a "neural network", an ANN, or an NN) in order
to transform a first color value in a first color coordinate system
into a second color value in a second color coordinate system.
The present invention also seeks to provide a technique for
multidimensional calibration of graphic arts reproduction
apparatus, which simplifies and greatly expedites the process of
calibration of graphic arts reproduction apparatus to faithfully
reproduce desired color and tone. Preferably, the technique
provides generally accurate calibration of the apparatus throughout
substantially the entirety of the range of colors producible by the
apparatus.
The present invention also seeks to provide an improved method for
comparing a first color value or set of color values from among a
first plurality of color values to a second color value or set of
color values from among a second plurality of color values which
may or may not be the same as the first plurality of color values.
Preferably, the method also comprises the step of transforming at
least some of the first set of color values in accordance with the
results of the comparing step.
There is also provided in accordance with a preferred embodiment of
the present invention, a technique for calibrating graphic arts
reproduction apparatus using color measuring apparatus (such as the
"Smart Scanner" available from Scitex Corporation, Herzlia, Israel,
colorimeters, densitometers, etc.) including the steps of providing
a transformation of or function, which may or may not have an
analytic form, from first color values to second color values and
employing the transformation to control operation of graphic arts
reproduction apparatus. The terms "transformation" and "function"
are used interchangeably throughout the present specification. The
transformation may be employed to provide a LUT (look up table)
which may be stored as employed as a color transformation tool.
The following procedures, among others, may be greatly simplified
and rendered more time efficient and effecting using preferred
embodiments of the present invention:
1. Incorporating a new color separation scanner (CSS), such as a
digital electronic color separation scanner, into an existing
reproduction system using automatic calibration that emulates the
tone and color reproduction of the existing system.
2. Compensating for a different printing or proofing machine or a
different setting on the same machine, by adjustment of the tone
and color transformation of a digital electronic color separation
scanner, or by adjustment of the digital representation of the
picture, such that the printed picture characteristics of tone and
color are nearly identical notwithstanding which printing machine
or setting is employed.
3. Creating upon a first substrate a duplication of an analog
representation of a color image upon a second substrate.
Preferably, both substrates are formed of the same medium or of
similar media.
4. Restoring an input copy for given color processing apparatus
from an available output copy thereof. Typically, the input and
output copies are hard copies. Preferably, the restored input copy,
if input to the color processing apparatus, will result in an
output copy substantially identical to the available output
copy.
5. Incorporating a new digital electronic color separation scanner
into an existing reproduction system using automation calibration
to achieve emulation of a UCR (under color removal), GCR (gray
component replacement) or UCA (under color addition) reproduction
produced by the existing system, or to emulate any other special
reproduction setting to which the existing system may be set.
6. Calibration of a color monitor display with reference to output
apparatus, thereby to provide a representation of a color image on
a color monitor display which is substantially identical to a hard
copy representation of that image processed on a given printing
device.
There is thus provided in accordance with a preferred embodiment of
the present invention a method for providing a neural network
including the steps of providing a neural network structure
including a plurality of neurons for receiving a first color value
from among a first set of color values which first color value is
to be transformed into a corresponding second color value from
among a second set of color values and for providing an output
indication of the corresponding second color value, and training
the neural network structure on a plurality of ordered pairs, each
ordered pair including a first color value from among the first set
of color values and a corresponding second color value from among
the second set of color values, one or both of the plurality of
first values and the plurality of second color values being a
systematic representation of the corresponding one of the first and
second sets of color values.
Further in accordance with a preferred embodiment of the present
invention, one of the first and second sets of color values is
defined within a color coordinate system and each region of a
predetermined size within the color coordinate system is
represented by at least one color value within the plurality of
color values corresponding to the set of color values defined
within the color coordinate system.
Further in accordance with a preferred embodiment of the present
invention, one of the first and second sets of color values is
defined within a color coordinate system which may be partitioned
into regions and each region within the partition is represented by
at least one color value within the plurality of color values
corresponding to the set of color values defined within the color
coordinate system.
Still further in accordance with the preferred embodiment of the
present invention, the first set of color values is identical to
the second set of color values.
Additionally in accordance with a preferred embodiment of the
present invention, each second color value, represented in visual
form, is substantially identical in appearance to the corresponding
first color value, represented in visual form.
Further in accordance with a preferred embodiment of the present
invention, the plurality of neurons includes an input layer of
neurons including at least one input neuron, at least one hidden
layer of neurons each including at least one hidden neuron, and an
output layer of neurons including at least one output neuron.
Additionally in accordance with a preferred embodiment of the
present invention, the first color value is also to be transformed
into a corresponding third color value from among a third set of
color values, the neural network structure is operative to provide
an output indication of the corresponding second and third color
values, the output layer of neurons includes at least a first
plurality of output neurons corresponding to the dimension of the
second color value and a second plurality of output neurons
corresponding to the dimension of a third color value and each
ordered pair includes a first color value and a corresponding
concatenation of a second color value and a third color value.
Still further in accordance with a preferred embodiment of the
present invention, the appearance of the second color value, when
represented using a predetermined first color output device, is
similar to the appearance of the third color value, when
represented using a predetermined second color output device.
Additionally in accordance with a preferred embodiment of the
present invention, each neuron in the at least one hidden layer and
in the output layer includes summing apparatus for computing a
weighted sum of a plurality of inputs.
Still further in accordance with a preferred embodiment of the
present invention, each neuron in the at least one hidden layer and
in the output layer also includes apparatus for computing a
nonlinear function of the output of the summing apparatus.
Additionally in accordance with a preferred embodiment of the
present invention, the nonlinear functions corresponding to
substantially all of the neurons in the at least one hidden layer
and in the output layer are equal.
Still further in accordance with a preferred embodiment of the
present invention, the neural network structure is a feed-forward
network structure.
Additionally in accordance with a preferred embodiment of the
present invention, each ordered pair is characterized in that there
is a predetermined relationship between the second color value and
the corresponding first color value.
Still further in accordance with a preferred embodiment of the
present invention, the plurality of regions includes regions of
non-equal size.
Additionally in accordance with a preferred embodiment of the
present invention, the plurality of regions includes regions of
equal size.
Further in accordance with a preferred embodiment of the present
invention, the method also includes the step of subsequently
employing the neural network for transforming a first color value
from the first plurality of color values into a second color value
from the second plurality of color values.
Still further in accordance with a preferred embodiment of the
present invention, the method also includes the step of employing
the second color value obtained by transforming the first color
value in order to control operation of a color processing system to
be calibrated.
Further in accordance with a preferred embodiment of the present
invention, at least one interneuron connection is defined between a
pair of neurons from among the plurality of neurons in the neural
network and the step of training includes the steps of providing
the first color value of an individual ordered pair to the neural
network, back-propagating an error value indicative of the
difference between the second color value of the individual ordered
pair and the output of the neural network for the first color
value, and modifying at least one of the at least one interneuron
connections.
Further in accordance with a preferred embodiment of the present
invention, at least one interneuron connection defines a weight
associated therewith and the step of modifying includes the step of
changing the value of the weight.
Still further in accordance with a preferred embodiment of the
present invention, the first set of color values is defined within
an individual one of the following coordinate systems: RGB, CMY,
CMYK, LHS, CieLab, RGBCMY, RGBCMYK, XYZ, DIN, Munsell, X*Y*Z*,
Ridgway, Oswald, Luv, Lu`v`, OSA, W.D.W, TCM.
Additionally in accordance with a preferred embodiment of the
present invention, the second set of color values is defined within
an individual one of the following coordinate systems: RGB, CMY,
CMYK, LHS, CieLab, RGBCMY, RGBCMYK, XYZ, DIN, Munsell, X*Y*Z*,
Ridgway, Oswald, Luv, Lu`v`, OSA, W.D.W, TCM.
There is also provided in accordance with a further preferred
embodiment of the present invention apparatus for providing a
neural network including a neural network structure including a
plurality of neurons for receiving a first color value from among a
first set of color values which first color value is to be
transformed into a corresponding second color value from among a
second set of color values and for providing an output indication
of the corresponding second color value, and apparatus for training
the neural network structure on a plurality of ordered pairs, each
ordered pair including a first color value from among the first set
of color values and a corresponding second color value from among
the second set of color values, one or both of the plurality of
first values and the plurality of second color values being a
systematic representation of the corresponding one of the first and
second sets of color values.
There is also provided in accordance with still a further preferred
embodiment of the present invention a neural network including a
trained neural network structure including a plurality of neurons
for receiving a first color value from among a first set of color
values which first color value is to be transformed into a
corresponding second color value from among a second set of color
values and for providing an output indication of the corresponding
second color value, wherein the trained neural network structure
was trained on a plurality of ordered pairs, each ordered pair
including a first color value from among the first set of color
values and a corresponding second color value from among the second
set of color values, one or both of the plurality of first values
and the plurality of second color values being a systematic
representation of the corresponding one of the first and second
sets of color values.
Further in accordance with a preferred embodiment of the present
invention, the second color value includes a black component and
the neural network structure is characterized in that at least some
of the color content of the first color value is transformed to the
black component of the second color value.
In accordance with still a further preferred embodiment of the
present invention, there is provided a method for transforming a
first color value from among a first set of color values into a
second color value from among a second set of color values, the
method including the steps of providing a trained neural network
structure including a plurality of neurons for receiving a first
color value from among the first set of color values which first
color value is to be transformed into a corresponding second color
value from among the second set of color values and for providing
an output indication of the corresponding second color value,
wherein the trained neural network structure was trained on a
plurality of ordered pairs, each ordered pair including a first
color value from among the first set of color values and a
corresponding second color value from among the second set of color
values, one or both of the plurality of first values and the
plurality of second color values being a systematic representation
of the corresponding one of the first and second sets of color
values, and employing the trained neural network structure in order
to transform a first color value from among the first set of color
values into a second color value from among the second set of color
values.
Further in accordance with a preferred embodiment of the present
invention, the method also includes the step of controlling
operation of a color processing system to be calibrated using the
second color value obtained in the employing step.
Still further in accordance with a preferred embodiment of the
present invention, the step of controlling includes the step of
using the color writing device to create upon a second substrate a
duplicate of an analog representation of a color image upon a first
substrate.
Additionally in accordance with a preferred embodiment of the
present invention, the step of controlling includes the step of
using the color processing system to create an input copy of a
color image which, when processed by the calibrated system, will
result in a given output copy of the color image.
Further in accordance with a preferred embodiment of the present
invention, the color processing system to be calibrated includes a
color reading device operative to convert an analog representation
of a color image into a digital representation thereof.
Still further in accordance with a preferred embodiment of the
present invention, the color processing system to be calibrated
includes a color writing device operative to convert a digital
representation of a color image into an analog representation
thereof.
Additionally in accordance with a preferred embodiment of the
present invention, the color writing device includes a color
monitor display.
According to yet a further preferred embodiment of the present
invention there is provided a method for constructing a look-up
table relating a first multiplicity of values to a second
multiplicity of values including the steps of providing an
artifical neural network relating the first multiplicity of values
to the second multiplicity of values, providing a plurality of LUT
addresses, operating the artificial neural network on the plurality
of LUT addresses, thereby to obtain a plurality of processed LUT
addresses, and storing the plurality of processed LUT addresses as
the contents of the look-up table.
Further in accordance with a preferred embodiment of the present
invention, the first and second multiplicities of values
respectively include first and second multiplicities of color
values.
Additionally in accordance with a preferred embodiment of the
present invention, the step of providing an artificial neural
network includes the steps of providing artificial neural network
training data representing the first and second multiplicity of
values and employing the artificial neural network training data to
train an artificial neural network.
There is also provided in accordance with a further preferred
embodiment of the present invention apparatus for constructing a
look-up table relating a first multiplicity of values to a second
multiplicity of values including an artificial neural network
relating the first multiplicity of values to the second
multiplicity of values, apparatus for operating the artificial
neural network on a plurality of LUT addresses, thereby to obtain a
plurality of processed LUT addresses, and apparatus for storing the
plurality of processed LUT addresses as the contents of the
LUT.
There is also provided in accordance with still a further preferred
embodiment of the present invention digital storage apparatus
including a representation of a look-up table relating a first
multiplicity of values to a second multiplicity of values, the
look-up table having been constructed by a method including the
steps of providing an artificial neural network relating the first
multiplicity of values to the second multiplicity of values,
providing a plurality of LUT addresses, operating the artificial
neural network on the plurality of LUT addresses, thereby to obtain
a plurality of processed LUT addresses, and storing the plurality
of processed LUT addresses as the contents of the look-up
table.
According to still a further preferred embodiment of the present
invention there is provided a method for constructing apparatus for
sampling the color processing characteristics of a color processing
device, the color processing device being operative to convert a
first representation of a color image into a second representation
thereof, the method including the step of repeating at least once
the steps of providing first and second representations of a color
image, the representations respectively including a first
multiplicity of first color values and a second multiplicity of
second color values corresponding thereto, the first and second
representations being characterized in that processing the first
representation with the color processing device defines the second
representation, providing an artificial neural network which, when
operated on each individual one of the second multiplicity of
second color values, gives a value substantially equal to the
corresponding one of the first multiplicity of first color values,
and operating the artificial neural network on the first
representation of the color image, thereby to provide a third
representation thereof.
There is provided in accordance with still a further preferred
embodiment of the present invention a system for constructing
apparatus for sampling the color processing characteristics of a
color processing device, the color processing device being
operative to convert a first representation of a color image to a
second representation thereof, the system including apparatus for
providing first and second representations of a color image, the
representations respectively including a first multiplicity of
first color values and a second multiplicity of second color values
corresponding thereto, the first and second representations being
characterized in that processing the first representation with the
color processing device defines the second representation, an
artificial neural network which, when operated on each individual
one of the second multiplicity of second color values, gives a
value substantially equal to the corresponding one of the first
multiplicity of first color values, and apparatus for operating the
artificial neural network on the first representation of the color
image, thereby to provide a third representation thereof.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will be understood and appreciated from the
following detailed description, taken in conjunction with the
drawings in which:
FIG. 1 is a conceptual illustration of a neural network of the feed
forward type and of a back propagation training method which
employs the generalized delta rule for training the neural
network.
FIGS. 2A-2B are schematic illustrations of a reiterative method for
providing an improved database for sampling the color processing
characteristics of color processing apparatus;
FIGS. 3A and 3B are schematic illustrations respectively of the
generation of a calibration transformation or function and its
employment in the incorporation of a new color separation scanner
or other color reading device into an existing reproduction system
employing automatic calibration in accordance with a preferred
embodiment of the present invention;
FIG. 3C is a conceptual illustration of a method which is a
generalization of the methods of FIGS. 3A and 3B;
FIG. 4A is a schematic illustration of compensation for a new
printing or proofing machine in accordance with a preferred
embodiment of the present invention;
FIG. 4B is a schematic illustration of an alternative method of
utilizing the calibration information provided by the technique of
FIG. 4A;
FIGS. 4C-4D illustrate a variation of the technique of FIG. 4A
useful for simultaneously calibrating a plurality of printing
systems, such as two printing systems, relative to a reference
printing system;
FIG. 4E illustrates a method for employing two printing systems
calibrated relative to a third, reference printing systems in order
to provide two respective output representations substantially
similar in appearance to one another and to the output of the
reference printing system;
FIGS. 5A, 5B and 5C are schematic illustrations which illustrate
respectively a calibration method and two alternative subsequent
uses therefore for generating duplications in accordance with a
preferred embodiment of the present invention;
FIGS. 6A-6E are schematic illustrations of a technique for
restoring an input copy from an output copy in accordance with a
preferred embodiment of the present invention;
FIGS. 7A and 7B are schematic illustrations of the generation of a
calibration transformation or function and its employment in
incorporation of a new digital electronic color separation scanner
in an existing system for producing UCR, GCR and UCA and any other
special setting tone and color reproductions, in accordance with
respective alternative embodiments of the present invention;
FIG. 8 is a schematic illustration of a method for calibration of a
color monitor display with reference to output apparatus in
accordance with a further preferred embodiment of the present
invention;
FIGS. 9A and 9B are color illustrations of the results of an
experiment performed in order to demonstrate an advantage of the
color transformation method of the present invention; and
FIG. 10 illustrates a very simple transformation function from a
one-dimensional space represented by the horizontal axis to a
second one-dimensional space represented by the vertical axis.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
It is an object of the present invention to provide a method and
apparatus for transforming colors in a first color coordinate
system into colors in a second color coordinate system.
It is a further object of the present invention to provide a
technique for multidimensional and preferably full range
calibration of graphic arts reproduction apparatus, which
simplifies and greatly expedites the process of calibration of
graphic arts reproduction apparatus to faithfully reproduce desired
tone and color. The calibration is accomplished by the following 2
steps:
(a) providing a database which may comprise a set of color values
representing a color image which it is sought to reproduce using
output apparatus employing a plurality of inks or other colorants
in amounts defined by the set of color values. A database which is
useful in implementing the present invention may be provided by
scanning the Q60 transparency, commercially available from Kodak
Corporation, using conventional scanning apparatus such as a Smart
Scanner, commercially available from Scitex Corporation. The
database may be provided, via suitable communication means such as
PC-Link, commercially available from Scitex Corporation, to a
suitable device for implementing a neural network training and
using system, such as an IBM PC.
In accordance with a preferred implementation of the present
invention, a database may be constructed as described in detail
below.
The second step in the calibration technique of a preferred
embodiment of the present invention is as follows:
(b) training a neural network (NN), also termed an "artificial
neural network" (ANN), to reflect the relationship between two
digital representations of the database. The neural network
preferably allows relatively accurate transformation procedures to
be carried out on color values which fall outside of the convex
hull spanned by the color values in the database. The neural
network may be employed to construct a look up table (LUT).
Alternatively, the neural network may be stored directly in any
suitable form.
If conditions are constant, a neural network may be trained once
and then employed for many subsequent color transformation tasks.
If conditions change, for example, if it is desired to change the
type of printing inks employed by a printing machine, then
additional training data may be supplied in order to retrain the
neural network.
Neural networks are discussed in the following publications:
Wasserman, Philip D. Neural Computing, Theory and Practice, Van
Nostrand Reinhold: New York, 1989.
Anderson, J. A. and Rosenfeld, E. Neurocomputing, MIT press,
1988.
Rumelhart, D. E. and McClelland, J. L. Parallel Distributed
Processing, MIT press, 1986.
The disclosures of the above publications and of the publications
cited therein are incorporated herein by reference.
THE STEP OF TRAINING A NEURAL NETWORK
A mathematical formulation of a typical problem is as follows:
given is a suitable number of values from a suitable color
coordinate system, such as 236 RGB values read by a color reading
device. Each value is an ordered 3-member set (r, g, b) defining
the respective quantities of Red, Green and Blue detected at each
of 236 locations upon a multicolored input image which is to be
read. The values r, g and b are scalars and typically 0<=r, g,
b<=255. Each of the 236 points of the multicolored input image
is to be represented by an output image in a suitable coordinate
system such as CMYK, corresponding to the printing inks which it is
desired to employ, which in this case are Cyan, Magenta, Yellow and
Black inks. An ANN is to be defined from the three dimensional (r,
g, b) color coordiante system to a four dimensional (c, m, y, k)
color coordinate system which will determine a quantity of each of
the four inks which is to be provided to reproduce any particular
color (r, g, b). A typical integer value range for each of the four
CMYK variables is [0,255]. Alternatively, the CMYK variables may be
provided or transformed into ink percentages.
Any suitable device can be employed to "read" the color values of
the database in any of the various embodiments described herein.
Inter alia, any of the following devices may be employed:
colorimeters, analog electronic color separation scanners, digital
electronic color separation scanners, densitometers, spectrum
analyzers.
Any suitable color reading device may be used as a calibration
reference, such as the Smart Scanner available from Scitex. In some
applications, such as Application No. 2 described hereinbelow, it
may be desirable to use a scanner whose colorimetric response is
similar to that of the human eye, or a scanner whose colorimetric
response is mathematically transformable to a response similar to
that of a human eye. Any coordinate system suitable for the
particular application may be used to represent the color values
(XYZ, RGB, etc.). Preferably, substantially all of the colors of
the reference color coordinate system should be distinguishable by
the device used as a calibration reference.
The procedure disclosed hereinbelow is relatively insensitive to
the selection of the particular set of 236 points. In particular,
the selected points need not be arranged at regular intervals and
do not even need to be distributed homogeneously. However, it is
generally preferable to provide a minimum density of data
distribution throughout the color coordinate system or space of
interest. It is appreciated that any suitable number of color
values may be employed.
Reference is now made to FIG. 1 which is a conceptual illustration
of a neural network of the feed forward type and of a back
propagation training method which employs the generalized delta
rule for training the neural network in order to transform a first
color value defined in a first color coordinate system into a
second color value defined in a second color coordiante system. It
is appreciated that the present invention is not limited to any
particular type of neural network or to any particular training
method and that use of the particular example illustrated herein is
intended to be merely illustrative and not limiting.
The training method of FIG. 1 employs training data 20 comprising a
plurality of ordered pairs, each ordered pair comprising a first
color value 22 defined in the first color coordinate system and a
corresponding second color value 24 defined in the second color
coordinate system. Each component of each first color value and
each component of each second color value is typically normalized
to the range of 0 to 1, rather than the range of the components of
the raw data which may be 0 to 255. For convenience, the first
color values 22 and first color coordinate system are termed herein
"RGB color values 22" and "RGB coordinate system", respectively,
whereas the second color values 24 and second color coordinate
system are termed "CMYK color values 24" and "CMYK coordinate
system", respectively. However, it is appreciated that the method
of FIG. 1 is suitable for transforming values from any first color
coordiante system to any second color coordinate system. First
normalized color value data 22 is also termed "input data" whereas
second normalized color value data 24 is termed "target output
data". The term "input data" is abbreviated as "IN" on some of the
drawings and the term "target output data" is abbreviated as "T.O."
on some of the drawings.
The appropriate method for providing suitable training data 20
depends upon the particular application. Several sample
applications of a trained neural network of the type shown and
described in FIG. 1 are described below. For each application, a
method of providing suitable training data 20 is described in
detail.
It is believed that the neural network 30 need not be of the feed
forward type and that training methods other than the back
propagation method may be employed.
The neural network 30 typically comprises an input layer 32 of
neurons, one hidden layer 34 of neurons and an output layer 36 of
neurons. It is appreciated that more than one hidden layer of
neurons may alternatively be provided. Each interconnection between
two neurons is assigned a weight defining the strength and
direction (positive or negative) of the relationship between the
two interconnected neurons. These weights are assigned initial
values such as values randomly selected from a suitable number set,
such as the set of real numbers from -1 to +1. Alternatively, the
initial values may be selected to be values which are believed, on
the basis of previous experience, to be relatively "good"
values.
According to a preferred embodiment of the present invention, a
bias neuron 37 for providing a constant output of a suitable value
such as 1, may be provided which is connected to the hidden and
output layers. The theory supporting provision of a bias neuron is
discussed, inter alia, in the above-referenced publication by
Wasserman entitled Neural Computing, Theory and Practice.
It is appreciated that the neural network 30 may have any suitable
configuration such as but not limited to the following
configuration:
Input layer: 3 nodes or neurons;
Hidden layer: 14 nodes;
Output layer: 4 nodes.
The RGB value 22 of each ordered pair from among the training data
20 is received by the input layer 32 of neurons. The neural network
computes a CMYK value 46 corresponding to the RGB value of the
current ordered pair.
The actual CMYK output 46 is compared to the desired CMYK value,
which is the second value 24 of the current ordered pair in the
training data 20. The result of the comparison is some error vector
corresponding in dimension to the dimension of output values 24 and
representing the deviation of the CMYK values 46 from the CMYK
values 24. The weights of at least one neuron interconnection
within the neuron network 30 are adjusted in accordance with the
error vector. The weights may be adjusted after each ordered pair
of alternatively a single adjustment of the weights may be made
only after an entire training epoch has terminated, in other words,
only after a predetermined number of the ordered pairs in training
data 20 have been processed.
Any suitable stopping criterion may be employed for terminating the
training stage. For example, training data may be processed once or
more until the adjustment or adjustments computed by the correction
algorithm are smaller than a predetermined value. Alternatively,
each value of the training data 20 may be presented a predetermined
number of times.
Once trained, the neural network 30 is operative to receive an RGB
value and output a CMYK value, in accordance with what may be
"learned" from training data set 20.
The neural network training method is now described in detail. In
the forgoing discussion, indices i, j and k are used for the
neurons of the hidden, input and output layers respectively. For
example, in the illustrated embodiment, i=1, . . . , 14; j=1,2,3;
and k=1,2,3,4.
The output H(i) of a neuron i in the hidden layer is computed as
follows:
where
f.sub.1 is preferably a singular and continuous function, such as
the sigmoid function exp (bx)/[exp (bx) +1], where the slope of the
function b, may be any suitable value such as 2;
I(j) is the value of input neuron j and W(i, j) is the weight of
the interconnection of input neuron j and hidden neuron i.
The output Out(k) of a neuron k in the output layer is computed as
follows:
where f.sub.2 is preferably a singular and continuous function,
such as a sigmoid function and W(k, i) is the weight of the
interconnection of output neuron k and hidden neuron i. Typically,
f.sub.2 is chosen to be the same as f.sub.1.
The error value Err(k) for a neuron k of the output layer is
computed as follows:
where IC(k) is the kth component of the CMYK component of the
current ordered pair from among the set 38 of ordered pairs.
A correction value to be added to W(k,i), D.sub.2 (k,i) is computed
as follows:
where f.sub.2 ' is the derivative of f.sub.2.
A correction value to be added to W(i,j), D.sub.1 (i,j) is computed
as follows:
where f.sub.1 ' is the derivative of f.sub.1.
The above computations are performed for each ordered pair from
among the set 20 of ordered pairs. According to a first preferred
embodiment of the present invention, the corrections to the
weights, termed herein D.sub.1 values and D.sub.2 values, may be
added to the weights after each individual element in the training
data is processed. According to an alternative preferred embodiment
of the present invention, the corrections to the weights computed
as each element in the training data is employed may be accumulated
until all elements in the training data have been used. Then, for
each input layer-hidden layer interconnection weight, an algebraic
sum of the accumulated D.sub.1 values corresponding thereto is
computed and added to that weight. For each hidden layer-input
layer interconnection weight, an algebraic sum of the accumulated
D.sub.2 values corresponding thereto is computed and added to that
weight.
It is appreciated that the particular neural network training
technique shown and described above is merely exemplary of possible
techniques and any suitable state of the art technique may be
employed. For example, momentum may be added and/or the step size
may be varied during training, all as explained in texts such as
the above-referenced publication by Wasserman.
THE STEP OF PROVIDING A DATABASE
As stated hereinabove, the method of the present invention includes
the step of providing a database comprising a representation of a
plurality of colors, which database may then be processed by color
processing apparatus. For example, the original database, whose
characteristics can be directly controlled by the operator, may be
the unprocessed RGB values and these values may be recorded, e.g.
on a transparency, and then scanned. The data which forms the basis
for the neural network training procedure described above with
reference to FIG. 1 will then be pairs of data elements, the first
data element being from the original database and the second data
element being the corresponding element from the processed data,
i.e. the transformed form of the first data element, obtained by
processing (recording and scanning) the original database.
It is therefore appreciated that a "good" database for sampling the
operation of color processing apparatus over a range or subrange
thereof has the property that, once processed by the color
processing apparatus, it will, for generally any region of a
predetermined size overlapping or contained within the range or
subrange, include at least a predetermined number of color values
located interiorly of that region. A more general requirement for a
"good" database is that, once processed, it is of a predetermined
degree of closeness to a "target" comprising a predetermined
plurality of color values. However, it is generally the case that
if a database which possessed this property prior to being
processed is subsequently processed by the color processing
apparatus, the processed data will no longer possess the desired
property but rather will be "distorted" due to the transformations
of the data induced by the color processing procedure.
The neural network training procedure described above can be used
in accordance with the method described hereinbelow to produce a
"good" database, in the sense set forth hereinabove, from an
initial database which may be far from possessing the desired
characteristic set forth hereinabove. According to one preferred
embodiment, the initial database, prior to being processed by the
color processing apparatus, comprises a set of points distributed
generally evenly throughout generally the entirety of the domain of
the apparatus.
The improvement process of the initial database may, if desired, be
continued iteratively until any desired degree of "quality", in the
sense described hereinabove, of the final database, is attained.
Typically, only three or less such iterations are necessary.
A preferred method in which the neural network training procedure
described hereinabove is used to provide an improved database will
now be described with reference to FIGS. 2A-2B, which are schematic
illustrations of the steps of the method. Each of steps (a)-(e) of
the method is designated in FIG. 2A by the appropriate letter. Step
(f) is illustrated in FIG. 2B.
It is appreciated that the method of FIGS. 2A-2B may be employed to
construct a first database which, once processed by given color
processing apparatus, provides a second, processed database which
defines a plurality of color values, each of which is substantially
equal to a corresponding one of any predetermined "target"
plurality of color values physically obtainable by means of the
color processing apparatus. The steps illustrated in FIG. 2A are as
follows:
(a) Provide an initial digital representation 50 of a color image,
the color image comprising a plurality of colored locations. The
digital representation 50 comprises a plurality of color values
such as RGB values, to be referred to as "RGB.sub.0 data", which
corresponds to the plurality of colored locations. Record the
RGB.sub.0 data with a color recording device 56 (such as a 4cast,
commercially available from DuPont) to obtain an analog
representation 52 of the color image comprising a plurality of
colored locations 54. Preferably, the initial digital
representation 50 of the initial color image will span generally
the entirety of the color space defined by the color recording
device.
Appendix B is a plurality of digital values which may be employed
to create a digital representation 50 of a color image comprising a
plurality of color patches. To create digital representation 50,
each digital value in Appendix B should be duplicated a
multiplicity of times, thereby to obtain a plurality of "patches",
respectively corresponding in color value to the digital values in
Appendix B, each patch comprising a multiplicity of pixels.
(b) Read the image 52 using desired input apparatus 58 and sample
the resulting digital representation of the patches or colored
locations 54, thereby to obtain a plurality 60 of color values such
as RGB values, to be referred to as "RGB.sub.1 data", which
correspond to the plurality of color locations 54. It is noted
that, generally, the RGB.sub.1 data obtained from the original
RGB.sub.0 data by recording and scanning will no longer have the
same values as the original RGB.sub.0 data. If the values of the
RGB.sub.1 data are not sufficiently close to a "target"
predetermined plurality of color values, follow steps (c) to (f)
below:
(c) Quantify the relationship between the input RGB.sub.1 data 60
and the target output RGB.sub.0 data 50 by pairing each RGB.sub.1
data element with the value of the corresponding RGB.sub.0 data
element and by using the neural network training method referred to
hereinabove. Training of the neural network may be performed by any
suitable neural network training unit 62, such as the neural
network training option in the software implemented neural network
training and using system provided herein and referenced Appendix
A.
The neural network 66 may be stored and operated by any suitable
means such as an IBM PC.
(d) Define RGB.sub.2 data 64 by passing the RGB.sub.0 values
through the trained neural network 66 or through a LUT constructed
from trained neural network 66, using the LUT construction method
shown and described below with reference to FIGS. 3A and 3B. The
RGB.sub.2 data is a digital representation of an "improved"
database (relative to the initial RGB.sub.0 database) in the sense
described hereinabove with reference to the term "good"
database.
(e) If an analog representation of the improved database is
desired, output the RGB.sub.2 file 64, which may be stored by any
suitable means, such as the storage module of the Smart Scanner,
using color output device 56 as a color printing device and using a
substrate 68 of a medium generally identical to the medium of the
substrate 52.
(f) If it is desired to continue the above procedure to obtain a
still further improved database, i.e. a database whose values are
still closer to the "target" predetermined plurality of color
values, continue as in FIG. 2B: Provide a digital representation of
the output 68 of (e), as in (b), using input apparatus 58, thereby
defining a plurality of color values such as RGB values, to be
referred to as "RGB'.sub.2 data" 80.
Construct a neural network quantifying the relationship between the
RGB'.sub.2 data 80 to the RGB.sub.2 data 64 and store it in module
66, as in (c) above.
Define and store RGB.sub.3 data 82 by operating the new neural
network on each of the RGB.sub.2 values 64, as in (d) above.
If desired, output the RGB.sub.3 data file, as in (e) above. The
resulting picture 84 is an analog representation of the still
further improved database.
The reiteration or loop of FIG. 2B may be repeated as many times as
desired to cause the resultant database to approach the "target"
predetermined plurality of color values to any desired degree of
closeness.
The results of a sample use of the method of FIG. 2A are now
described:
Appendix C discloses the plurality of digital values which
correspond to the color values of each of a plurality of color
patches in a digital file which was employed as digital
representation 50 of FIG. 2A. In other words, to obtain the digital
file which was employed in the present experiment as digital
representation 50 of FIG. 2A, each digital value in Appendix C may
be duplicated a multiplicity of times, thereby to obtain a
plurality of "patches", respectively corresponding in color value
to the digital values in Appendix C, each patch comprising a
multiplicity of pixels.
One iteration of the method of FIG. 2A was performed on the digital
"patches" file corresponding to Appendix C. The parameters of the
resulting ANN 66 are appended hereto and are referenced Appendix D.
The digital database 64 resulting from the single iteration of the
method of FIG. 2A is appended hereto and is referenced Appendix E.
If it is desired to use Appendix E in the method of FIG. 2B, the
following step is performed:
The color values of Appendix E are employed to create digital
representation 68 of FIG. 2A comprising a plurality of color
patches. To create digital representation 68, each digital value in
Appendix E should be duplicated a multiplicity of times, thereby to
obtain a plurality of "patches", respectively corresponding in
color value to the digital values in Appendix E, each path
comprising a multiplicity of pixels. The resulting digital
"patches" is recorded by recorder 56 and the method of FIG. 2B may
then be employed.
The database of Appendix E is particularly useful in conjunction
with a Smart Scanner, commercially available from Scitex
Corporation, Herzlia, Israel.
An alternative to the database provision method shown and described
above with reference to FIGS. 2A and 2B is now described:
As explained above, an initial database which may be useful in
implementing the present invention may be provided by scanning the
Q60 transparency, commercially available from Kodak Corporation,
using conventional scanning apparatus such as a Smart Scanner,
commercially available from Scitex Corporation. Appendix F is a
plurality of color values sampled from a digital representation of
the Q60 transparency, obtained by scanning with the Smart Scanner.
One color value was sampled from each patch of the Q60
transparency.
The database may be provided, via suitable communication means such
as PC-Link, commercially available from Scitex Corporation, to a
suitable device for implementing a neural network training and
using system, such as an IBM PC.
It is appreciated that the method of providing a data base and the
method of training a neural network, both as shown and described
hereinabove, have a wide variety of applications when used
independently or in conjunction with one another. For example, the
method of providing a database described hereinabove is useful not
merely for the purpose of constructing a neural network as
described hereinabove, but also in any situation in which it is
desired to sample the functioning or the characteristics of color
processing apparatus, e.g. in quality control and repeatability
test situations such as those presented in the foregoing examples.
It is appreciated that the foregoing examples are merely
illustrative of possible applications in which it is desired to
sample the functioning or the characteristics of color processing
apparatus.
EXAMPLE A
A typical situation in which the method of providing a database as
shown and described hereinabove is useful in quality control is
that of a printing machine or other output apparatus which is found
to produce somewhat varying output as a function of fluctuating
environmental factors. A database designed to sample the
characteristics of the printing machine, constructed in accordance
with the method shown an described hereinabove, may be printed
periodically on the printing machine. The database is preferably
constructed to sample the printing of colors which are known to be
sensitive or problematic when printed on that particular machine.
The hard copy is then scanned and a suitable neural network is
constructed to compensate for any drift which may have occurred
relative to a previously defined standard.
EXAMPLE B
The method of providing a database may also be useful in quality
control of color reading apparatus such as scanners. For example,
if a scanner is thought to be defective, a database designed to
sample the characteristics of that scanner, constructed in
accordance with the method shown and described hereinabove, may be
scanned by the putatively defective scanner and the result compared
to the results of scanning the same database using results from a
scanner known to be properly functional. The database is preferably
constructed to sample the scanning of colors which are known to be
sensitive or problematic when scanned on that particular
scanner.
It is appreciated that the above examples are merely illustrative
of possible quality control applications. The term "quality
control" is here employed to describe any application in which the
quality of performance of color processing apparatus is of
interest. More generally, it also applies to any situation in which
it is of interest to sample the performance of color processing
apparatus.
EXAMPLE C
A typical situation in which the method of providing a database as
shown and described hereinabove is useful in repeatability control
is that of a scanner which is suspected of being improperly
functional for a certain subregion (or the entire region) of the
output space, comprising a plurality of colors. The database
provision method shown and described hereinabove may be employed to
provide a transparency or other representation which, when scanned,
will be mapped onto the subregion in question. This transparency
may be used to test the scanner and effect suitable corrective
procedures thereupon. It is appreciated that this example is merely
illustrative of possible repeatability control applications. The
term "repeatability control" or "repeatability testing" is here
employed to describe any application in which the repeatability of
performance of color processing apparatus over time and/or over
changing environmental conditions is of interest.
A number of color image processing applications in which a neural
network, such as a neural network trained using a database provided
in accordance with the method of FIGS. 2A and 2B, may usefully be
employed, will be described in detail herein. The color image
processing applications described herein are intended to be merely
illustrative of the range of possible applications and are not
intended to limit the range of color processing applications in
which a neural network may be employed using the methods disclosed
herein.
It is appreciated that only one or a few embodiments of each of the
applications disclosed is described in detail hereinbelow, and that
the details of implementation described herein are merely
illustrative and by way of example, and that the embodiments
described herein may be modified in any suitable manner. For
example, any of the applications herein may be implemented on any
suitable computer, such as an IBM PC, by performing the required
transformation on the digital output file of any ECSS. Measurements
of the database may be carried out automatically, using the
automatic calibration function provided on the Smart Scanner,
commercially available from Scitex Corporation, Herzlia, Israel.
Alternatively, the database may be measured manually, using any
suitable equipment such as a spectrum analyzer. The measured data
may then be input into the computer either automatically or
manually.
APPLICATION #1
Calibration of a First Color Scanner with Reference to a Second
Color Scanner
Reference is now made to FIGS. 3A and 3B which illustrate
respectively the generation of a calibration transformation and its
employment in the incorporation of a new digital electronic color
separation scanner into an existing reproduction system employing
automatic calibration in accordance with a preferred embodiment of
the present invention.
Conventionally, an existing reproduction work shop that purchases a
new electronic color separation scanner (CSS) already owns one or
more CSSs. During years of work and interaction with their
customers, the shop has developed its own unique tone and color
reproduction parameters that characterize the reproductions they
produce. The tone and color reproduction parameters may depend on
at least the following factors:
The type of originals employed, i.e. the brand and type of
transparency or reflective copy;
The color separation scanner employed and its calibration;
The plotting system employed;
The printing system employed; and Aesthetic considerations.
The introduction of a new ECSS normally changes the tone and color
reproduction parameters that are realized. A long and tedious
process of adjustment of the new ECSS is normally required,
involving numerous adjustments by trial and error. Normally the
tone and color reproduction parameters existing prior to
introduction of the new ECSS are never fully realized.
In accordance with the present invention, the trial and error
techniques currently in use are replaced by a fully- or, if
desired, semi-automated well-defined and generally algorithmic
technique.
In accordance with a preferred embodiment of the present invention,
as illustrated in FIG. 3A, there is provided a substrate, such as a
transparency, bearing an analog representation of a color image 110
which typically comprises a plurality of colored locations 112.
Preferably, the color image will comprise a "good" database
constructed in accordance with the database provision method shown
and described hereinabove. Here a "good" database is one which,
once scanned by the scanner 114 of FIG. 3A, has a predetermined
pattern such as a pattern in which there is a minimum density of
data in every area of interest. The predetermined pattern may, for
example, be a generally even distribution throughout generally the
entirety of the physically producible color space, if it is desired
to sample generally the entirety of the color space. Therefore,
when constructing the color image 110 in accordance with the
database provision method of FIG. 2, the scanner 114 should
preferably be used to scan the color image 52. Alternatively,
scanner 116 can be used.
The color image 110 is scanned both by an existing ECSS 114 which
it is sought to emulate and by the new digital ECSS 116. From the
existing ECSS 114 a digital representation 118, comprising color
values (preferably CMYK values) each corresponding to an individual
one of the locations 112, is obtained. These values relate to the
amounts of each colorant to be provided by a printing machine.
From the DECSS 116, a digital representation 120 of the locations
112, comprising color values (preferably RGB values) corresponding
to each location 112 is provided.
It is appreciated that references to RGB values and CMYK values,
etc. throughout the present specification are intended to be
examples of suitable color coordinates which can be replaced by any
other suitable color coordinates, such as XYZ or LAB coordinates.
Furthermore, there need not be exactly three input dimensions, or
exactly three or four output dimensions. Any suitable number of
dimensions may be employed.
A neural network training unit 122 receives pluralities of
corresponding color values 118 and 120 and computes a weight for
each pair of connected nodes of a neural network relating input
color values 120 and output color values 118 in accordance with the
neural network training procedure shown and described hereinabove
with reference to FIG. 1. Color values 120 are used as the first
color values 22 of training data set 20 of FIG. 1. Color values 118
are used as the second color values 24 of training data set 20 of
FIG. 1. The trained neural network 124 may be stored in any
suitable storage device, such as the TCR module of the scanner 116,
and may be employed to calibrate the scanner.
Alternatively, the trained neural network may be employed to
construct a LUT 127 relating the colorant values 118 to the RGB
values 120. A preferred method for constructing a LUT using an
artificial neural network comprises the following steps:
(a) providing RGB addresses of the LUT.
For example, the following set of values may be employed as
addresses. The set of values includes all triplets in which each of
the three components in the triplet has one of the following
values: 0, 16, 32, . . . , 255.
______________________________________ 0 0 0 16 0 0 32 0 0 . . .
255 0 0 0 16 0 16 16 0 32 16 0 . . . 255 16 0 . . . 0 255 0 16 255
0 32 255 0 . . . 255 255 0 . . . 0 255 255 16 255 255 32 255 255 .
. . 255 255 255 ______________________________________
(b) The above addresses are normalized by dividing by 255.
(c) The normalized addresses are provided to the trained neural
network as input.
(d) The output obtained from the neural network is multiplied by a
suitable factor such as 255 and is stored as the contents of the
LUT in any suitable storage unit such as in the TCR module of the
scanner 116.
Appendix A is a software implementation of a preferred method for
training an ANN and for constructing a LUT based on the trained
ANN.
It is appreciated that the applicability of the above method for
employing an artificial neural network to construct a LUT and for
subsequently employing the LUT as a transformation tool, rather
than employing the artificial neural network itself as a
transformation tool, is not limited to situations in which the
input values and output values of the artificial neural network are
color values. Rather, it is believed that the above method for
constructing a LUT and subsequently employing it to replace the ANN
as a transformation tool is suitable for transformations between
any type of values to any type of values.
It is appreciated that the neural network training unit and the LUT
construction unit described in the present specification may be
formed as a single unit, such as a computer program.
As a result of the foregoing technique, an input of any particular
input material to the DECSS will produce DECSS outputs with
substantially identical CMYK values as those produced on the
existing ECSS from the same input material.
FIG. 3B illustrates the reproduction of input material using the
existing ECSS 114 as opposed to the calibrated DECSS 116. The DECSS
116 scans the input 128, resulting in a first digital
representation 130 thereof, which is then converted by the trained
neural network 124, or by a LUT 127 representing the trained neural
network 124, into a second digital representation 132 of the input
128, representing the required amounts of each colorant. It is seen
that the digital representation 134 of the image 128 resulting from
scanning by the ECSS 114 will normally be substantially identical
to the output 132, as scanned by the DECSS 116.
If the neural network 124 was employed to construct a LUT, the
color values of the first digital representation which do not
appear in the LUT constructed by LUT construction unit 126 may be
interpolated therefrom, using standard methods, such as those
disclosed in chapter 2 of J. Stoer, Introduction to Numerical
Analysis, Springer-Verlag, New York, 1980.
It is appreciated that the same or similar interpolation methods
may be used in all of the applications of the present invention
shown and described subsequently. The interpolation methods are
preferably carried out automatically by suitable hardware, such as
that commercially available from Zoran Corporation, Santa Clara,
Calif., USA, or from INMOS Limited, Bristol, UK. A particular
advantage of directly employing an ANN as a color transformation
tool rather than constructing a LUT on the basis of the ANN and
using the LUT as a construction tool, is that no interpolation
procedures are necessary. All output values are directly computed
by the ANN.
In accordance with the embodiment of FIG. 3A, the ECSS 114 output
of color values 118, corresponding to the color patches 112, can be
stored as a digital file and can be transmitted to neural network
training unit 122 by any suitable technique, such as via a cable
connection, or by employing magenta tape or other medium.
The above-described technique is not limited to automatic reading
of colorant values. These values may be manually read by one from
the scanner. The operator may then input into the neural network
training unit 122, as via a keyboard or via any other suitable
input means, a list of RGB values and corresponding colorant
values.
Reference is now made to FIG. 3C which is a conceptual illustration
of a generalization of the method of FIGS. 3A and 3B. The method
and apparatus of FIG. 3C are useful in any application in which it
is desired to train an ANN 140 to mimic an existing color
transformation which may be represented in any suitable form such
as in the form of a LUT 142 for transforming a first color value
from among a first plurality of color values such as RGB color
values, into a second color value from among a second plurality of
color values such as CMYK color values.
Preferably, the method for training ANN 140 comprises the following
steps:
a. Provide a database 144 which suitably represents the first
plurality of color values. A database may be provided by scanning
the Q60 transparency, commercially available from Kodak
Corporation, as explained above. Alternatively, a database may be
constructed using the database construction method shown and
described herein with reference to FIGS. 2A-2B.
b. Transform the database values using, in the present embodiment,
the LUT 142, thereby to obtain a set of LUT-processed database
values 146, such as CMYK values.
c. Compute a weight for each pair of connected nodes of ANN 140,
employing the method of FIG. 1, and using database 144 as the input
training data and CMYK data 146 as the target output training
data.
APPLICATION #2
Output to Output Calibration
Reference is now made to FIG. 4A which is a schematic illustration
of calibration procedures for producing a first printing system
output substantially identical to the output from a second printing
system.
The embodiment of FIG. 4A is particularly useful in calibrating a
proofing machine, used to prepare a single copy of a reproduction
for preliminary proofing purposes, to emulate a printing machine
which it is intended to use to produce the final reproduction. The
state of the art technology, such as the Cromalin (registered
trademark) system available from DuPont (U.K.) Limited,
Hertfordshire, UK, produces a reproduction which may differ
substantially from the output of the printing machine that the
proofing system is intended to emulate. Consequently, the proof
must be evaluated by an expert who can judge the quality thereof
while attempting to mentally adjust for the expected discrepancies
between proof and eventual printed reproduction. The present
invention enables the proofing machine to be accurately and
algorithmically calibrated so as to emulate the printing
machine.
Since they may exist colors that can be printed by the final
printing machine but cannot be printed by the proofing machine
using any combination of colorants, it is desirable to choose a
proofing machine that is compatible with the printing machine. For
example, the Cromalin (registered trade mark) proofing system
available from DuPont is generally compatible with offset printing
machines. Otherwise, "unprintable" colors may be dealt with using
any suitable technique, such as the techniques described in the
above-referenced article by Stone et al (particularly pages 275-279
thereof), the disclosure of which is incorporated herein by
reference.
A further application is when a printing machine needs to be
replaced or when it is desired to add an additional printing
machine to an existing workshop. Since the new machine may be of a
different brand, type or model than the old machine, it is
typically found that printing with the same colorant values on the
new machine will produce a color with a different appearance.
Therefore, it is generally the case that the new printing machine
must be adjusted manually, by a trial and error process, until the
reproductions obtained therefrom roughly resemble the reproductions
obtained from the existing machine. It is typically impossible to
obtain complete concordance between the appearances of the
reproductions produced by the first and second machines.
The different appearances obtained from different printing or
proofing machines may be the result of at least the following
reasons: different colorant materials employed, different
technologies employed (offset, gravure, web, Cromalin (registered
trade-mark), ink-jet, heat transfer, etc.), dot shape of half-tone
film or plates, room temperature, humidity, etc.
Comparison of the results from the respective printing devices is
preferably carried out in a CIE (Commission International
d'Eclairage) standard color space but may also be carried out in
any other suitable color space.
A preferred procedure for using a graphic arts reproduction system
comprising a first printing device as a reference in order to
calibrate a graphic arts reproduction system comprising a second
printing device is the following, described with reference to FIG.
4A:
a. Provide a first database 210 and a second database 212 for the
first, reference, and second, to be calibrated, printing devices
214 and 216 respectively. The two databases comprise first and
second pluralities of colorant values, preferably CMYK values.
Preferably, databases 210 and 212 are "good" databases for sampling
the operations of output devices 214 and 216 respectively, in the
sense that, once printed by printers 214 and 216 respectively and
scanned by the scanner 222, each database has a predetermined
pattern such as a pattern in which there is a minimum density of
data in every area of interest. The predetermined pattern may, for
example, be a generally even distribution throughout generally the
entirety of the physically producible color space, if it is desired
to sample generally the entirety of the color space.
The two databases may be constructed in accordance with the
database provision method shown and described hereinabove. When
constructing database 210, using the database provision method of
FIGS. 2A-2B, the printer 214 should be used. When constructing
database 212, the printer 216 should be used. Preferably, the
pluralities of colorant values 210 and 212 include only colorant
values that are actually used in reproduction tasks, by printers
214 and 216 respectively.
b. Databases 210 and 212 are printed by printing devices 214 and
216 respectively. The resulting images 218 and 220 respectively are
scanned by a color reading device 222 such as the Smart Scanner
available from Scitex. The digital representations of images 218
and 220 respectively resulting from the scanning thereof are
referenced as 224 and 226. Digital representations 224 and 226 each
comprise a plurality of color values, such as RGB values. In some
applications it may be desirable to convert the pluralities of RGB
values 224 and 226 to corresponding pluralities of CIELab, XYZ
values or values from another suitable coordinate system, using
known techniques.
c. Neural network training unit 228 receives pluralities of
corresponding color values 226 and 212 as input data and target
output data respectively, and trains a neural network 229
accordingly in accordance with the method shown and described
herein with reference to FIG. 1. Neural network training unit 228
is constructed and operative in accordance with the neural network
training procedure shown and described hereinabove. The ANN 229
trained by ANN training unit 228 is stored in storage unit 230 and
outputs the amounts of cyan, magenta, yellow and black inks
required to print, using printing device 216, a color to be read as
a given RGB value by color reading device 222.
d. The ANN 229 trained by training unit 228 is operated on the RGB
values of representation 224, resulting in a plurality 231 of CMYK
values. For each CMYK value of database 210, the corresponding
C'M'Y'K' value in digital representation 231 represents the amounts
of the colorants required to produce, by means of printer 216, a
colored location which would be read by color reading device 222 as
a value substantially equal to the corresponding RGB value in
digital representation 224.
e. A second ANN training unit 232 is operative to receive
pluralities of color values 210 and 231 as input data and target
output data respectively and to train an ANN 233 quantifying the
relationship between the color values 210 and the color values 231.
The ANN 233 may be received by LUT construction unit 234 and used
to construct a LUT 236. Alternatively, the ANN 233 may be stored in
any other suitable manner, as by storing the set of weights and
network parameters defining ANN 233, such as the size of the
layers. The weights and parameters of ANN 233 or the LUT 236
representing ANN 233 may be stored in any suitable storage device
237, such as a disc.
ANN 233 therefore represents the conversions of the amounts of
cyan, magenta, yellow and black inks required to print using
printing device 216, such that the output will appear to the color
reading device 222 to be substantially identical to the RGB values
read from the unconverted values of c, m, y and k printed by
printing device 214.
According to a first preferred embodiment, when scanning image
representations 218 and 220, the white point is selected to be as
close as possible to the white-point CMY values of the
corresponding printers 214 and 216 respectively. If the selected
white point cannot coincide exactly with the corresponding
white-point CMY value, a slightly higher white point is typically
selected. All other controls are put on their default setting.
According to an alternative preferred embodiment, the white point
is taken on a blank portion of the white paper or background. All
other controls are put on their default setting.
It is appreciated that the most appropriate selection of the white
point may vary as a function of the particular application and of
the particular graphic arts reproduction system employed.
Preferably, color image representations 218 and 220 are each
automatically scanned, thereby to define a plurality of color
values corresponding to a plurality of colored locations into which
each image is divided. Any suitable procedure may be employed to
accomplish this, which procedure may comprise the steps of:
automatically passing from pixel to pixel of the color image while
reading and storing the color values of each pixel, defining a
plurality of colored locations each comprising a plurality of
pixels, and averaging or otherwise combining the values of at least
some of the pixels in each colored location, thereby to define a
color value for each colored location. A commercially available
function for automatically scanning an analog representation of
color patches is the automatic calibration function provided on the
Smart Scanner, commercially available from Scitex Corporation.
Once constructed, LUT 236 or trained ANN 233 may be utilized in at
least two different ways:
(i) If it is desired to print, on printer 216, an image represented
as a digital file originally intended for printing by printer 214
so that its appearance to the color reading device 222 will be
substantially as when the digital file is printed on printer 214,
the digital file is passed through LUT 236 or trained ANN 233 and
the resulting transformed digital file is printed on printer 216.
The results of printing the digital file on printer 214 and
subsequently reading it using color reading device 222 are
substantially identical to the results that would be obtained by
printing the transformed file on printer 216 and subsequently
reading it using color reading device.
(ii) Reference is made to FIG. 4B which illustrates modification of
an RGB-to-CMYK LUT 260 incorporated in a color reading device 233
which may be identical to scanner 222 of FIG. 4A. LUT 260 is
suitable for use in conjunction with printing device 214. It is
desired to modify LUT 260 and thereby to obtain a modified
RGB-to-CMYK LUT 262 which, when loaded onto scanner 223 and used in
conjunction with printing device 216 will result in pictures
substantially identical to those produced by scanner 223 located
with LUT 260 and printing device 214, where the term "substantially
identical" implies that pictures produced by the two processes will
be "seen" as substantially identical by a scanner.
As shown in FIG. 4B, LUT 236 or ANN 233 is operated on the values
of LUT 260, transforming each CMYK value intended for printer 214
to a CMYK value suitable for printer 216, thereby to obtain LUT
262. Consequently, the result 264 of scanning a particular image
265 using scanner 222 loaded with LUT 260 and subsequently printing
with printer 214 are substantially the same as the result 266 of
scanning the image using scanner 222 loaded with LUT 262 and
subsequently printing with printer 216. This implies that a scanned
representation of picture 264 will comprise generally the same
values as a scanned representation, using the same scanner, of
picture 266.
It is appreciated that the operation of LUT 236 on a body of data
is substantially equivalent to the operation of ANN 233 on the same
body of data, since the structure of LUT 236 reflects the structure
of ANN 233.
Reference is now made to FIGS. 4C-4D which illustrate a method and
apparatus for simultaneously calibrating a plurality of printing
systems, such as two printing systems, relative to a reference
printing system.
A preferred method for simultaneously calibrating two or more
printing system is as follows:
a. Steps a-d of the method of FIG. 4A are carried out in order to
initiate calibration of printer 216 relative to printer 214.
b. Steps a-d of the method of FIG. 4A are carried out, using the
same reference scanner output 224 but replacing CMYK database 212
with CMYK database 242 and printer 216 with printer 246. In FIG.
4C, the output of printer 246 is referenced 250, the output of
scanner 222 is referenced 256, the ANN trained by training unit 228
is referenced 259, and the output of trained ANN 259 is referenced
261. Database 242 may be selected to appropriately sample the
operation of printer 246 in the same way that database 212 is
selected to appropriately sample the operation of printer 216.
c. Referring now to FIG. 4D, pluralities 231 and 261 of CMYK values
are concatenated, thereby to provide a plurality 270 of 8
dimensional vectors, each vector comprising the four components of
the corresponding element in CMYK data 231 and the four components
of the corresponding element in CMYK data 261.
d. The plurality 270 of 8 dimensional data is provided as target
output to ANN training unit 272. The input data is CMYK data 210.
The ANN training unit 272 trains an ANN 273 whose output layer
typically comprises 8 neurons. The configuration parameters and
weights of ANN 273 may be stored in any suitable storage means 237
such as the TCR module of a scanner. Alternatively or in addition,
a LUT 276 may be constructed based upon the ANN 273, using the LUT
construction method shown and described above with reference to
FIGS. 3A and 3B. The contents of the LUT is typically 8
dimensional, corresponding to the two four-dimensional ink
coordinate values stored at each location of the LUT.
Reference is now made to FIG. 4E which illustrates a method for
employing the two printing systems 216 and 246 calibrated relative
to the third, reference printing system 214 in order to provide two
respective output representations substantially similar in
appearance to one another and to the output of the reference
printing system. A sample application of the method of FIG. 4E is
when a Chromalin proof has been produced using a Dupont Chromalin
system and it is desired to print the image represented by the
proof using both offset and gravure printing processes and to
ensure that the appearances of the proof and of the outputs of the
offset and gravure processes are substantially identical. In this
example, the reference printing system may be the gravure printing
machine or the offset printing machine.
A CMYK file 278 is provided which is a digital representation to be
printed on printing system 214, and on printing systems 216 and
246, while preserving the appearance of the CMYK file 278 when
printed on printing system 214. The CMYK file 278 is provided as
input to trained ANN 273, thereby providing an output file 280
which comprises a plurality of 8 dimensional values (CMYKCMYK). The
CMYKCMYK values 280 are split into first and second pluralities 282
and 284 of CMYK values which are then printed on printers 216 and
246 respectively. The appearances of the outputs 288 and 290 from
printers 216 and 246 respectively are substantially identical to
the appearance of analog representation 286 which was printed
directly from CMYK file 278, using reference printing system
214.
APPLICATION #3
Duplication of Originals
Reference is now made to the schematic illustrations of FIGS. 5A
and 5B, which illustrate an embodiment of the invention useful in
producing duplications of images existing as hard copies on a
particular medium (such as but not limited to a transparency or
reflective copy). It is noted that a half-toned printed picture can
be duplicated entirely analogously to what will be described
herein, except that the picture may be descreened, using
conventional techniques.
Conventional descreening techniques are described in Marquet, M.,
"Dehalftoning of negatives by optical filtering,", Optica Acta 6,
404-405, 1959; Marquet, M. and J. Tsujiuchi, "Interpretation of
Particular Aspects of Dehalftoned Images," Optica Acta 8, 267-277,
1961; and Kermisch, D. and P. G. Roetling, "Fourier Spectra of
Halftone Screens", J. Opt. Soc. Amer. 65, 716-723, 1975. The
disclosures of these documents are incorporated herein by
reference.
A preferred method for providing for duplication of images
represented on a given medium will now be described. Steps (a)-(d)
are illustrated in FIG. 5A. Step (e) comprises two alternative
methods for duplicating a given image once steps (a)-(d) have been
carried out, illustrated in FIGS. 5B and 5C respectively.
a. Provide a first digital representation 310 of a color image,
typically comprising a first plurality of RGB values, using any
suitable procedure such as the database provision method shown and
described hereinabove. Here a "good" database 310 is one which is
suitable for sampling the operation of recorder 312 used in
conjunction with recording medium 314 and scanner 316, as explained
hereinabove in the section on database construction, and is
preferably constructed in accordance with the method of FIGS.
2A-2B. Therefore, when using the database provision method of FIGS.
2A-2B to construct the database 310, the scanner 316 and the
recorder 312 should be used for scanning and recording the initial
database.
b. Place a substrate 314 of the desired medium in a color recorder
312 such as a 4cast commercially available from DuPont. According
to a preferred embodiment of the present invention, the medium of
the substrate 314 is the same as the medium of the original 326
(FIG. 5B) which it is desired to duplicate. Load the color
recording apparatus 312 with the digital file 310, thereby to
provide an analog representation 315 corresponding to the digital
representation 310 of the color image.
c. Read the analog representation 315 using a color reading device
316 such as an analog ECSS or a DECSS, thereby to obtain a second
digital representation 318 of the color image, preferably
comprising a second plurality of RGB values corresponding to the
plurality 310 of RGB values.
d. Input digital representations 310 and 318 to ANN training unit
320, which is operative to train an ANN 321 to transform the
plurality of color values 318 to the plurality of color values 310
in accordance with the ANN training procedure described
hereinabove. As explained above with reference to FIG. 1, neural
network training unit 320 receives pluralities of corresponding
color values 22 and 24 and computes a set of weights for a neural
network based upon the relationship between the color values 22 and
the color values 24. In the present embodiment, color values 318
are used as the first color values 22 of training data set 20 of
FIG. 1. Color values 310 are used as the second color values 24 of
training data set 20 of FIG. 1.
The trained ANN 321 computed by ANN training unit 320 may be stored
in any suitable storage unit such as the TCR module of scanner 316.
Alternatively, the ANN may be received by LUT construction unit
322. LUT construction unit 322 is operative to construct a LUT 324
relating the RGB values 318 to the RGB values 310 as dictated by
ANN 321 and to store the LUT 324 in the TCR module of the scanner
316. The LUT 324 or the trained ANN 321 may now be used as
follows:
e. Reference is made to FIG. 5B. Given a substrate 326 (preferably
of the same medium as substrate 314) bearing an analog
representation of a color image 327, and when it is sought to
duplicate the color image 327 onto a second substrate 328
(preferably of the same medium as substrate 326), the image 327 is
scanned by the scanner 316 whose TCR module contains the LUT 324 or
the trained ANN 321, thereby to obtain a digital representation 330
of the color image. The digital representation is then recorded by
color recording apparatus 312, thereby to obtain a substantially
accurate duplicate 332 of the original color image 327 on substrate
328.
Alternatively, the color image 327 may be reproduced as in FIG. 5C.
As shown, the image 327 is scanned by the scanner 316 using only
the color separation unit 334, thereby to define a digital
representation 336, preferably comprising a plurality of RGB
values, of image 327. The digital representation 336 is stored in
storage unit 338.
The weights and configuration parameters of ANN 321 trained by ANN
training unit 320 may be stored in any suitable storage unit 340,
such as the memory of a suitable computer. Alternatively, ANN 321
may be employed to construct LUT 324. ANN 321 then operates on
digital representation 336 which is read from storage unit 338,
thereby to provide a modified digital representation 330 of image
327. Digital representation 330 is then recorded by color recording
apparatus 312, thereby to obtain a substantially accurate duplicate
332 of the original color image 327 on substrate 328.
If desired, certain of the above steps can be performed manually.
Specifically, the RGB color values of the patches 314 may be
manually measured with a color separation scanner and then manually
input into ANN training unit 320, as by a keyboard, instead of
being scanned.
According to an alternative embodiment, the image 327 on the
substrate 326 is scanned itself to provide digital representation
310 (FIG. 5A). This embodiment is particularly useful in certain
applications as it employs precisely those colors required for the
duplication of the particular image 327.
APPLICATION #4
Reconstruction of Input from Output
Reference is now made to FIGS. 6A-6E, which illustrate a further
embodiment of the present invention useful in reconstructing a hard
copy produced using a given tone and color reproduction system.
FIG. 6A describes a standard reproduction process of an image 412
which is printed as a reflective copy 430. If the original
transparency 412 is unavailable, it can be reconstructed using
either the processed digital file 424 or the reflective output
430.
FIG. 6B describes an application in which it is desired to create a
single image comprising the tree in picture 412 and the sun in
picture 414, and to represent it upon a single substrate, thereby
to obtain a single representation 432 (such as a reflective copy)
of both the sun and the tree. It may be desired to provide
transparencies of the representation of the combined image in which
the tree resembles the tree in the original picture 412 and the sun
resembles the sun in the original picture 414. Preferably, the
medium of the original picture 412 is substantially identical to
the medium of the original picture 414.
FIG. 6C illustrates a preferred method of reconstructing the input
copy 412 assuming that a LUT 422 was constructed on the basis of
the ANN used to transform the RGB representation 418 of the image
412 into a CMYK representation 424, using the LUT construction
method of FIGS. 3A and 3B, and assuming that LUT 422 and digital
file 424 are still available.
First, LUT 422 is inverted, using known methods such as those
disclosed on page 267 of the above referenced article by Stone et
al, thereby to provide an inverted LUT 434. LUT 434 is then
operated on digital file 424, thereby to provide a digital file
436, typically comprising a plurality of RGB values, which values
are substantially identical to the plurality of RGB values 418
scanned from the input copy 412 (FIG. 6A).
Alternatively, the LUT 422 inversion step may be replaced by the
step of providing an ANN for transforming CMYK representation 424
into RGB representation 418 of the image 412, particularly if the
ANN used to transform the RGB representation 418 of the image 412
into a CMYK representation 424 was not employed to create a LUT.
The LUT 434 operation step is then replaced by the following
steps:
i. Providing a CMYK-RGB database which may be constructed using the
database provision method shown and described above with reference
to FIGS. 2A-2B.
ii. Providing an ANN for transforming CMYK values into RGB values,
using the ANN training method shown and described above with
reference to FIG. 1 and using the database provided in step (i) as
training data. The CMYK values are the input data and the RGB
values are the target output data.
iii. Operating the CMYK-to-RGB ANN provided in step ii on CMYK
representation 424.
Subsequently an operator 437 is constructed, which, when operated
on digital file 436, will result in a digital file 438 which when
recorded on a substrate 440 (preferably of the same medium as the
original 412) by a recorder 442, will result in an analog
representation which has the following property: If scanned by
scanner 416, analog representation 440 will provide a digital
representation 443 substantially identical to digital file 436 (and
digital file 418). Preferably, the analog representation also has
the property of appearing to the human eye to have substantially
the same tone and color as the original 412. The operator 437 may
comprise an ANN, as in the illustrated embodiment, or a LUT
constructed to correspond to the ANN, using the LUT construction
method shown and described above with reference to FIGS. 3A and
3B.
A preferred method of training an ANN 437 with at least the former
property and typically both properties has been shown and described
hereinabove with reference to FIG. 5A, in which the ANN with the
desired properties is referenced as ANN 321. Alternatively, the ANN
437 may be replaced by a LUT constructed in accordance with the
ANN, using the LUT construction method described above with
reference to FIGS. 3A-3B.
A preferred method of reconstructing the input copy 412 from the
output copy 430 when digital file 424 is not available, whereas the
printed picture 430 of FIG. 6A is available, is illustrated in
FIGS. 6D and 6E. As shown, the method comprises providing a
database 444, which is preferably a "good" database for sampling
the operation of printer 428 in conjunction with scanner 416 and
which typically comprises a plurality of CMYK values. The database
444 is printed by printer 428, thereby to provide a printed
representation 446 such as a reflective copy and is subsequently
scanned by scanner 416, thereby to provide a digital file 450.
Alternatively, digital file 450 may be predetermined and database
444 may be constructed therefrom using the database construction
method shown and described hereinabove with reference to FIGS.
2A-2B.
ANN training unit 452 receives corresponding pluralities of color
values 450 and 444 and trains an ANN relating input RGB values 450
to target output CMYK values 444, using the method described herein
with reference to FIG. 1. The weights and configuration parameters
of the ANN may be stored in any suitable form, thereby to enable
the ANN itself to be directly employed as a color transformation
tool. Alternatively, the ANN may be employed to construct a LUT
454, which is then stored and employed as a color transformation
tool.
As explained above with reference to FIG. 1, neural network
training unit 452 receives pluralities of corresponding color
values 450 and 444 and constructs a set of weights for a neural
network approximating the relationship between the color values 450
and the color values 444. In the present embodiment, color values
450 are used as the first color values 22 of training data set 20
of FIG. 1. Color values 444 are used as the second color values 24
of training data set 20 of FIG. 1.
As shown in FIG. 6E, output copy 430 is scanned by scanner 416 and
the resulting digital file 456, typically comprising RGB values, is
passed through the stored form 454 of the ANN, thereby to provide a
digital file 458 preferably comprising a plurality of CMYK values.
The plurality 458 of CMYK values, when output by printer 428, will
result in a hard copy 460 of the original image which is
substantially identical to the hard copy 430. The digital file 458
is substantially identical to digital file 424 of FIG. 6A.
Therefore, digital file 458 may be employed to restore the original
transparency 412 using the procedure of FIG. 6C.
The color recording apparatus 442 may comprise any suitable color
recording apparatus, such as the 4cast plotter available from
DuPont.
The computations described hereinabove need not be carried out by
the scanner but may alternatively be carried out by any suitable
computation means, typically a standard computer such as an IBM PC,
which may communicate with the remainder of the apparatus using any
suitable conventional communication method.
APPLICATION #5
Calibration of a First Color Separation Scanner with Reference to a
Second Color Separation Scanner on a Special Setting
The following embodiment of the present invention is useful when it
is desired to calibrate a scanner or other color reading device
relative to a reference scanner/reading device on a special setting
such as but not limited to GCR, UCR, UCA, etc. This embodiment is
particularly useful if the operator is relatively unfamiliar with
the special setting.
Reference is now made to FIG. 7A which illustrates an embodiment of
the present invention useful in incorporating a new DECSS into an
existing TCR system comprising a currently used ECSS (or DECSS) on
a special setting.
It is appreciated that, by putting the currently used ECSS onto its
special setting, an ANN may be constructed which will allow the new
DECSS to emulate the existing TCR system, by using the method of
FIGS. 3A and 3B shown and described hereinabove. However, normally,
a modified implementation of an ANN or of a look up table
constructed in accordance therewith is undesirable since operators
generally find it difficult to perceive and interpret the special
setting CMYK values in the course of subsequent operator controlled
tone and color adjustment. Therefore, it is preferable to initially
scan the image with a scanner located with a "regular" ANN or LUT
in order to enable the operator to carry out the desired tone and
color modifications. Once the modifications have been completed,
the modified color values may be converted to the special setting
values, thereby to implement the calibration of the scanner to be
calibrated with reference to the special setting of the reference
scanner.
A preferred procedure for calibrating a first color scanner with
reference to a second color scanner on a special setting comprises
the following steps:
a. The existing scanner 510 is put onto its normal setting N and an
analog representation 512 of a color image comprising a plurality
of colored locations 514 is scanned, thereby to obtain a digital
representation 516 comprising a plurality of color values,
typically CMYK values, corresponding to the plurality of colored
locations 514.
The color image 512 is preferably a "good" database constructed in
accordance with the database provision method shown and described
hereinabove. Here a "good" database 512 is one whose values are as
close as desired to a "target" predetermined plurality of color
values. For example, database 512 may comprise a database which is
so constructed that it samples the operation of scanner 510 on its
special setting in the subrange in which use of a special rather
than normal setting makes a substantial difference. Construction of
such a database is explained hereinabove in connection with the
database construction method of FIGS. 2A-2B.
b. The existing scanner 510 is put onto the desired special setting
S and the same color image is scanned, thereby to obtain a digital
representation 518 comprising a plurality of color values,
typically CMYK values, corresponding to the plurality of colored
locations 514.
c. Digital representations 516 and 518 are input to ANN training
unit 520, which is operative to train an ANN 521 relating the
plurality of input color values 516 to the plurality of target
output color values 518 in accordance with the ANN training
procedure shown and described hereinabvoe.
Typically, as explained above with reference to FIG. 1, neural
network training unit 520 receives pluralities of corresponding
color values 516 and 518 and constructs a set of weights for a
neural network approximating the relationship between the color
values 516 and the color values 518. In the present embodiment,
color values 516 are used as the first color values 22 of training
data set 20 of FIG. 1. Color values 518 are used as the second
color values 24 of training data set 20 of FIG. 1.
The weights and configuration parameters of ANN 521 may be stored
in a suitable storage device such as the TCR module of a scanner,
thereby to enable the ANN 521 to be directly employed as a color
transformation tool. Alternatively, ANN 521 may be employed by a
LUT construction unit 522 to construct a LUT 524 representing the
relationship between CMYK values 518 to CMYK values 516. LUT 524
may be stored in any suitable storage device such as in the TCR
module of the scanner 526.
d. When it is desired to use the new DECSS 526 to scan an input
copy 528, the input 528 is scanned with the scanner 526, thereby to
obtain a digital representation 530 of the input 528. The RGB
(typically) values of digital representation 530 are typically
converted using either ANN 124 of FIG. 3A or the standard LUT 127
constructed by LUT construction unit 126 of FIG. 3A. The result is
a second digital representation 532 of input 528, preferably
comprising a plurality of CMYK values which are "standard" in that
they are familiar to a human operator accustomed to working on a
normal setting and thus easily modifiable by the operator.
e. Desired tone and color manipulations may be carried out by a
human operator, resulting in modifications of digital
representation 532 and of subsequent versions thereof.
Once the operator has completed the step of manipulating tone and
color, the ANN 521 or a stored form of ANN 521 such as LUT 524 is
employed to convert each of the normal setting CMYK values of the
digital representation 532 to the corresponding special setting
CMYK values, resulting in a final digital representation 536 of the
input 528, which is substantially identical to the digital
representation of input 528 which would result by scanning input
528 with scanner 510 on its special setting and performing the same
operator-input tone and color manipulations.
An alternative method is illustrated in FIG. 7B, in which a LUT is
employed in the TCR module as a color transformation tool. In the
embodiment of FIG. 7B, following the execution of tone and color
modifications by the operator, the modified CMYK values of LUT 127
may be converted, thereby to define a converted LUT 538, by using
the conversion stored in LUT 524 or by operating ANN 521 on LUT
127. LUT 538 may be stored in the TCR module of the scanner 526.
Digital representation 530 may then be directly converted by LUT
538, preferably on the fly, to provide the final digital
representation 536.
It is noted that here as throughout the present specification, the
ANN training unit and the parameters of the ANN constructed thereby
may be stored in the memory of any suitable commercially available
computing means, such as an IBM PC communicating with a color
reproduction system such as a Macintosh computer, commercially
available from Apple, Inc. and running Photoshop software,
commercially available from Adobe Systems, Inc., Mountainview,
Calif., USA, via commercially available communication means such as
the public domain KERMIT communication package in conjunction with
an RS232 cable. Alternatively, the ANN training unit and the
parameters of the ANN constructed thereby may be stored integrally
with a color reproduction system.
APPLICATION #6
Calibration of a Color Monitor Display with Reference to Output
Apparatus
Reference is now made to FIG. 8 which is a schematic illustration
of a method for calibration of a CRT with reference to output
apparatus. The objective is to provide an analog representation
610, on a CRT display 616, of a color image, which representation
resembles a hard copy representation 612 of the color image output
from a printing device 214.
The present method and apparatus are generally similar to the
method and apparatus of FIG. 4A, where a printing device 216
(rather than a CRT) is calibrated with reference to output
apparatus 214. Identical reference numerals are employed to
reference identical elements in FIGS. 4A and 8 to facilitate
understanding of the similarity. The distinguishing elements of the
method and apparatus of FIG. 8 will now be discussed.
As shown in FIG. 8, an optical interface 620 is required to enable
scanner 222 to receive input from CRT 616. The particular interface
required varies according to the scanner 222. For example, the
Scitex Smart Scanner may be optically coupled to the screen of the
monitor 616 by mechanically disconnecting and removing the color
separation head of the scanner from the interior of the scanner
while maintaining the electrical wiring connections and placing the
head in front of the monitor.
A plurality 618 of RGB values is provided which is a "good "
database in the sense that it samples the operation of color
monitor 616 such that, once represented on the monitor, the values
cover substantially the entirety of the space physically producible
by the color monitor 616 at least a predetermined density. The RGB
values 618 are preferably displayed one after the other on the CRT
screen 616 and are received one at a time by the scanner 222.
Synchronization of the scanner with the monitor is required. This
procedure is provided on the Smart Scanner available from
Scitex.
As in Application #2, it may be desirable to convert pluralities of
RGB values 224 and 226 to XYZ values or values from any other
suitable coordinate system, using conventional apparatus and
techniques, such as those described in P. G. Engeldrum, "Almost
Color Mixture Functions", Journal of Imaging Technology, 14(4),
August 1988, and in references 2 and 5-7 cited therein. The
disclosures of this article and of all references cited therein are
incorporated herein by reference. Also, it is appreciated that any
suitable color reading device may replace the scanner 222.
If desired, RGB values 226 may be read in CMC (Color Mixture
Curves) form by optical interface 620. The filter arrangement of
the normally used color separation head of the Smart Scanner may be
replaced by a CMC filter arrangement which emulates the human eye.
CMC filter arrangements and methods for constructing them are
described in the above referenced article entitled "Almost color
mixture functions" as well as in references 2, 5 and 6 thereof.
The method of FIG. 8 is most easily understood by comparison to the
method of FIG. 4A. In the method of FIG. 4A, CMYK values 212 and
RGB values 226 are employed as target output data and input data,
respectively, to train a first ANN 229. Also in the method of FIG.
4A, a plurality of RGB values 226 is provided by scanner 222 which
reads analog representation 220 provided by printer to be
calibrated 216 which inputs CMYK values 212. In contrast, in the
method of FIG. 8, CMYK values 212 are printed on the reference
printer 214 and are used as target output data to train first ANN
229, the input data being RGB values 224. Therefore, in FIG. 8, ANN
229 is a tool for transforming given RGB values into CMYK values,
such that, once the CMYK values are printed on reference printer
214 and are subsequently read by scanner 222, the resulting RGB
values will be generally identical to the given RGB values.
Furthermore, when the second ANN 233 is trained in FIG. 4A, the
target output data is the plurality 231 of CMYK values, which is
the output of first ANN 229 which receives RGB input 224. The
training input data for ANN 233 in the method of FIG. 4A is the
plurality of CMYK values used for printing on the reference printer
214. In contrast, in the embodiment of FIG. 8, ANN 233 is trained
using RGB values 618 as target output data and the CMYK values 231
are the input data for the training process.
Preferably, the illumination of analog representations 610 and 612
should be such that their respective white areas will be of
substantially the same brightness.
It is appreciated that ANN 233 may be employed itself as a color
transformation tool to transform CMYK values 614 into RGB values
suitable for display on monitor 616. Alternatively, ANN 233 may be
employed in order to construct a LUT 236, using the LUT
construction method described above in connection with FIGS. 3A and
3B. The LUT 236 then replaces ANN 233 as the tool for transforming
CMYK values 614 into RGB values suitable for display on monitor
616.
Reference is now made to FIGS. 9A-9B which are color illustrations
of the results of an experiment performed in order to demonstrate a
particular advantage of the color transformation method shown and
described herein, in which the color transformation is stored as a
neural network, relative to state of the art color transformation
methods in which the color transformation is stored as a LUT.
A particular advantage of the color transformation method shown and
described herein is that, generally, it does not introduce
discontinuities, whereas state of the art color transformations
stored as LUTs do generally introduce discontinuities when a linear
interpolation process is employed.
In state of the art methods, the color transformation function,
which is generally defined from a relatively large plurality of
points such as an entire color space, is stored as a LUT having a
relatively small number of discrete points. The color
transformation between the points of the LUT is not stored but
rather is computed by a suitable method such as linear
interpolation. Therefore, a LUT representation of a color
transformation, even a relatively smooth color transformation, is
generally not smooth but rather includes breaking points.
Introduction of discontinuities by color transformation methods in
which the color transformation is stored in a LUT may be understood
with reference to FIG. 10 which illustrates a very simple
transformation function from a one-dimensional space represented by
the horizontal axis to a scanned one-dimensional space represented
by the vertical axis. The transformation function is indicated by a
dotted line 1000, and a LUT, storing the transformation, is
indicated by a solid line 1002. The points of the LUT are
referenced A, B, C, . . . . Points B, C, E, G and H are seen to be
breaking points because their right slope is far from equal to
their left slope. For example, point B is a breaking point because
the slope of segment AB is considerably larger than the slope of
segment BC. Therefore, if a color vignette, which includes gradual
color variations, is transformed using the LUT 1002,
discontinuities will be apparent at the locations of the color
vignette corresponding to the breaking points of LUT 1002.
Referring back to FIGS. 9A-9B, the experiment was conducted as
follows:
a. A plurality of RGB values, read from a Q60 transparency,
commercially available from Kodak Corporation, was read by a Scitex
Smart Scanner loaded with an RGB-CMYK LUT, thereby to obtain a
plurality of RGB-CMYK pairs.
b. An ANN was trained by presenting it with the plurality of
RGB-CMYK pairs obtained in step a, using the method shown and
described above with reference to FIGS. 3C and 1.
c. A set of RGB LUT addresses is provided, such as the RGB LUT
addresses specified above in step (a) of the LUT construction
method described with reference to FIGS. 3A-3B. The set of RGB LUT
addresses is passed through the trained ANN of step b, thereby to
obtain a plurality of CMYK values.
d. An RGB digital file was constructed in which, for each pixel,
R=G=B. The digital file comprised 256 pluralities of adjacent
lines, each plurality of adjacent lines comprising a suitable
number of identical lines, each line comprising a plurality of
identical pixels. The following is a representation of the R values
of the first line of each of the pluralities of adjacent lines
within the RGB digital file:
______________________________________ First plurality: 255, 255, .
. . , 255 Second plurality: 254, 254, . . . , 254 . . 255th
plurality: 1, 1, . . . , 1 256th plurality: 0, 0, . . . , 0
______________________________________
Since, for each pixel, R=G=B, the above is also a representation of
the B values and of the G values of the first line of each
plurality of adjacent lines within the RGB digital file.
It is noted that all pixel color values within any given row of the
RGB digital file are identical. Also, the pixel color values of the
RGB digital file vary linearly between pluralities of adjacent
lines. The difference between pixel color values in adjacent
pluralities of lines is 1.
e. The RGB file from d was transformed twice, once using the ANN of
step b and once using the LUT of step C. The two transformations
resulted in two CMYK files. FIGS. 9A and 9B are printed copies of
the CMYK file resulting from the ANN transformation procedure and
the CMYK file resulting from the LUT transformation procedure,
respectively.
It is seen that the vignette of FIG. 9A, which was created using an
ANN, as shown and described in the present invention, substantially
retains the smoothness of the precursor RGB digital file in step d.
In contrast, the vignette of FIG. 9B, which was created using a
LUT, does not retain the smoothness of the precursor RGB digital
file in step d. Instead, it is possible to observe points of
discontinuity 1010 at the vertical locations of the color vignette
corresponding to the breaking points of the LUT.
The results of the experiment show that points of discontinuity
substantially do not occur when the transformation tool employed is
an ANN, whereas points of discontinuity do occur when the
transformation tool employed is a LUT, even though the LUT itself
was created using the ANN.
Although the method of employing an ANN as shown and described in
the present invention, is believed to have certain advantages
relative to state of the art LUT methods, such as smoothness of
appearance of the printed product. However, use of a LUT
corresponding to an ANN as a color transformation tool may, in
certain situations, be more efficient than direct use of the ANN
itself as a color transformation tool.
A particular advantage of employing an artificial neural network as
a color transformation tool is that the artificial neural network
is implementable in hardware. For example, a commercially available
chip suitable for designing a hardware implementation of a neural
network is the analog neural network IC 80170 chip by Intel
Corporation, Santa Clara, Calif., USA.
Reference is now made to Appendix A which is a software
implementation of ANN training and operating apparatus constructed
in accordance with a preferred embodiment of the present invention
and operative in conjunction with an IBM PC, using the DOS
operating system and a Turbo Pascal package, commercially available
from Borland International, Scotts Valley, Calif., USA.
It will be appreciated by persons skilled in the art that the
present invention is not limited to what has been particularly
shown and described hereinabove. Rather, the scope of the present
invention is defined only by the claims that follow: ##SPC1##
______________________________________ APPENDIX B Original.rgb:
data for possible original database Patch # R G B
______________________________________ 1 0 0 0 2 0 0 0 3 3 3 0 4 3
0 3 5 0 3 3 6 2 2 2 7 5 6 7 8 12 2 2 9 2 12 2 10 12 12 2 11 2 2 12
12 12 2 12 13 2 12 12 14 12 12 12 15 17 3 3 16 3 17 3 17 3 3 17 18
16 16 16 19 27 26 25 20 34 3 3 21 37 6 7 22 51 3 3 23 48 16 16 24
59 26 25 25 3 34 3 26 5 38 7 27 3 51 3 28 16 48 16 29 27 58 25 30 3
3 34 31 5 6 39 32 3 3 50 33 16 16 48 34 27 26 57 35 5 5 5 36 5 5 5
37 3 3 68 38 5 6 71 39 3 3 85 40 16 16 80 41 27 26 89 42 5 38 39 43
16 48 48 44 27 58 57 45 3 68 3 46 5 70 7 47 3 85 3 48 16 80 16 49
27 90 25 50 37 38 7 51 48 48 16 52 59 58 25 53 37 6 39 54 48 16 48
55 59 26 57 56 68 3 3 57 69 6 7 58 85 3 3 59 80 16 16 60 91 26 25
61 102 3 3 62 101 6 7 63 119 3 3 64 112 16 16 65 123 26 25 66 69 38
7 67 80 48 16 68 91 58 25 69 10 10 10 70 10 10 10 71 69 6 39 72 80
16 48 73 91 26 57 74 37 6 71 75 48 16 80 76 59 26 89 77 37 38 39 78
59 58 57 79 37 70 7 80 48 80 16 81 59 90 25 82 3 102 3 83 5 102 7
84 3 119 3 85 16 112 16 86 27 122 25 87 5 70 39 88 16 80 48 89 27
90 57 90 5 38 71 91 16 48 80 92 27 58 89 93 3 3 102 94 5 6 103 95 3
3 119 96 16 16 112 97 27 26 121 98 5 6 135 99 3 3 136 100 3 3 152
101 16 16 144 102 27 26 153 103 16 16 16 104 16 16 16 105 5 38 103
106 16 48 112 107 27 58 121 108 5 70 71 109 16 80 80 110 27 90 89
111 5 102 39 112 16 112 48 113 27 122 57 114 5 134 7 115 3 136 3
116 3 153 3 117 16 144 16 118 27 154 25 119 37 102 7 120 48 112 16
121 59 122 25 122 37 70 39 123 59 90 57 124 37 38 71 125 59 58 89
126 37 6 103 127 48 16 112 128 59 26 121 129 69 6 71 130 80 16 80
131 91 26 89 132 69 38 39 133 91 58 57 134 69 70 7 135 80 80 16 136
91 90 25 137 21 21 21 138 21 21 21 139 101 38 7 140 112 48 16 141
123 58 25 142 101 6 39 143 112 16 48 144 123 26 57 145 133 6 7 146
136 3 3 147 153 3 3 148 144 16 16 149 155 26 25 150 165 6 7 151 170
3 3 152 187 3 3 153 176 16 16 154 187 26 25 155 133 38 7 156 144 48
16 157 155 58 25 158 133 6 39 159 144 16 48 160 155 26 57 161 101 6
71 162 112 16 80 163 123 26 89 164 101 38 39 165 123 58 57 166 101
70 7 167 112 80 16 168 119 90 23 169 69 102 7 170 80 112 16 171 26
26 26 172 26 26 26 173 91 122 25 174 69 70 39 175 91 90 57 176 69
38 71 177 91 58 89 178 69 6 103 179 80 16 112 180 91 26 121 181 37
6 135 182 48 16 144 183 59 26 153 184 37 38 103 185 59 58 121 186
37 70 71 187 59 90 89 188 37 102 39 189 59 122 57 190 37 134 7 191
48 144 16 192 59 154 25 193 5 166 7 194 3 170 3 195 3 187 3 196 16
176 16 197 27 186 25 198 5 134 39 199 16 144 48 200 27 154 57 201 5
102 71 202 16 112 80 203 27 122 89 204 5 70 103 205 31 31 31 206 31
31 31 207 16 80 112 208 27 90 121 209 5 38 135 210 16 48 144 211 27
58 153 212 5 6 167 213 3 3 170 214 3 3 187 215 16 16 176 216 27 26
185 217 5 6 199 218 3 3 204 219 3 3 221 220 16 16 208 221 27 26 217
222 5 38 167 223 16 48 176 224 27 58 185 225 5 70 135 226 16 80 144
227 27 90 153 228 5 102 103 229 16 112 112 230 27 122 121 231 5 134
71 232 16 144 80 233 27 154 89 234 5 166 39 235 16 176 48 236 25
186 53 237 5 198 7 238 3 204 3 239 36 36 36 240 36 36 36 241 3 221
3 242 16 208 16 243 27 218 25 244 37 166 7 245 48 176 16 246 59 186
25
247 37 134 39 248 59 154 57 249 37 102 71 250 58 122 89 251 37 70
103 252 59 90 121 253 37 38 135 254 59 58 153 255 37 6 167 256 48
16 176 257 59 26 185 258 69 6 135 259 80 16 144 260 91 26 153 261
69 38 103 262 91 58 121 263 69 70 71 264 91 90 89 265 69 102 39 266
91 122 57 267 69 134 7 268 80 144 16 269 91 154 25 270 101 102 7
271 112 112 16 272 123 122 25 273 42 42 42 274 42 42 42 275 101 70
39 276 123 90 57 277 101 38 71 278 123 58 89 279 101 6 103 280 112
16 112 281 123 26 121 282 133 6 71 283 144 16 80 284 155 26 89 285
133 38 39 286 155 58 57 287 133 70 7 288 144 80 16 289 155 90 25
290 165 38 7 291 176 48 16 292 187 58 25 293 165 6 39 294 176 16 48
295 187 26 57 296 197 6 7 297 204 3 3 298 221 3 3 299 208 16 16 300
219 26 25 301 229 6 7 302 238 3 3 303 241 2 2 304 251 2 1 305 253 3
0 306 253 0 3 307 47 47 47 308 47 47 47 309 255 3 3 310 241 12 2
311 251 12 2 312 241 2 12 313 251 2 12 314 241 12 12 315 251 12 12
316 253 17 3 317 253 3 17 318 240 16 16 319 251 26 25 320 197 38 7
321 208 48 16 322 219 58 25 323 197 6 39 324 208 16 48 325 219 26
57 326 165 6 71 327 176 16 80 328 187 26 89 329 165 38 39 330 187
58 57 331 165 70 7 332 176 80 16 333 187 90 25 334 133 102 7 335
144 112 16 336 155 122 25 337 133 70 39 338 153 86 57 339 133 38 71
340 155 58 89 341 52 52 52 342 52 52 52 343 133 6 103 344 144 16
112 345 155 26 121 346 101 6 135 347 112 16 144 348 123 26 153 349
101 38 103 350 123 58 121 351 101 70 71 352 123 90 89 353 101 102
39 354 123 122 57 355 101 134 7 356 112 144 16 357 123 154 25 358
69 166 7 359 80 176 16 360 91 186 25 361 69 134 39 362 91 154 57
363 69 102 71 364 91 122 89 365 69 70 103 366 91 90 121 367 69 38
135 368 91 58 153 369 69 6 167 370 80 16 176 371 91 26 185 372 37 6
199 373 48 16 208 374 59 26 217 375 57 57 57 376 57 57 57 377 37 38
167 378 59 58 185 379 37 70 135 380 59 90 153 381 37 102 103 382 59
122 121 383 37 134 71 384 59 154 89 385 37 166 39 386 59 186 57 387
37 198 7 388 48 208 16 389 59 218 25 390 5 230 7 391 3 238 3 392 2
241 2 393 12 241 2 394 2 251 2 395 3 253 0 396 0 253 3 397 3 255 3
398 12 251 2 399 2 241 12 400 12 241 12 401 2 251 12 402 12 251 12
403 17 253 3 404 3 253 17 405 16 240 16 406 25 246 25 407 5 198 39
408 31 187 57 409 62 62 62 410 62 62 62 411 27 218 57 412 5 166 71
413 16 176 80 414 27 186 89 415 5 134 103 416 16 144 112 417 27 154
121 418 5 102 135 419 16 112 144 420 27 122 153 421 5 70 167 422 16
80 176 423 27 90 185 424 5 38 199 425 16 48 208 426 27 58 217 427 5
6 231 428 3 3 238 429 2 2 241 430 12 2 241 431 2 12 241 432 12 12
241 433 2 2 251 434 3 0 253 435 0 3 253 436 3 3 255 437 12 2 251
438 2 12 251 439 12 12 251 440 16 3 253 441 3 17 253 442 31 31 213
443 68 68 68 444 68 68 68 445 27 26 249 446 5 38 231 447 3 34 253
448 3 51 253 449 16 48 240 450 27 58 249 451 5 70 199 452 16 80 208
453 27 90 217 454 5 102 167 455 16 112 176 456 27 122 185 457 5 134
135 458 16 144 144 459 27 154 153 460 5 166 103 461 16 176 112 462
27 186 121 463 5 198 71 464 16 208 80 465 27 218 89 466 5 230 39
467 3 253 34 468 3 253 51 469 16 240 48 470 27 250 57 471 37 230 7
472 34 253 3 473 50 251 4 474 48 240 16 475 59 250 25 476 48 179 50
477 73 73 73 478 73 73 73 479 59 218 57 480 37 166 71 481 59 186 89
482 37 134 103 483 59 154 121 484 37 102 135 485 59 122 153 486 37
70 167 487 59 90 185 488 37 38 199 489 59 58 217 490 37 6 231 491
34 3 253 492 51 3 253 493 48 16 240 494 59 26 249 495 69 6 199 496
80 16 208 497 91 26 217
498 69 38 167 499 91 58 185 500 69 70 135 501 91 90 153 502 69 102
103 503 91 122 121 504 70 135 72 505 91 154 89 506 69 166 39 507 88
187 50 508 69 198 7 509 80 208 16 510 92 195 39 511 78 78 78 512 78
78 78 513 101 166 7 514 112 176 16 515 123 186 25 516 101 134 39
517 123 154 57 518 101 102 71 519 123 122 89 520 101 70 103 521 123
90 121 522 101 38 135 523 123 58 153 524 101 6 167 525 112 16 176
526 123 26 185 527 133 6 135 528 144 16 144 529 155 26 153 530 133
38 103 531 155 58 121 532 133 70 71 533 155 90 89 534 133 102 39
535 155 122 57 536 133 134 7 537 144 144 16 538 155 150 23 539 165
102 7 540 176 112 16 541 184 115 26 542 166 71 40 543 187 90 57 544
152 49 76 545 83 83 83 546 83 83 83 547 187 58 89 548 165 6 103 549
176 16 112 550 187 26 121 551 197 6 71 552 208 16 80 553 219 26 89
554 197 38 39 555 219 58 57 556 197 70 7 557 208 80 16 558 219 90
25 559 229 38 7 560 253 34 3 561 253 51 3 562 240 48 16 563 251 58
25 564 229 6 39 565 253 3 34 566 253 3 51 567 240 16 48 568 251 26
57 569 229 6 71 570 253 3 68 571 253 3 85 572 240 16 80 573 251 26
89 574 229 38 39 575 241 49 49 576 249 58 53 577 229 70 7 578 224
74 21 579 88 88 88 580 88 88 88 581 253 85 3 582 240 80 16 583 251
90 25 584 197 102 7 585 208 112 16 586 219 122 25 587 197 70 39 588
219 90 57 589 197 38 71 590 219 58 89 591 197 6 103 592 208 16 112
593 219 26 121 594 165 6 135 595 176 16 144 596 187 26 153 597 165
38 103 598 187 58 121 599 165 70 71 600 187 90 89 601 165 102 39
602 187 122 57 603 165 134 7 604 176 144 16 605 187 154 25 606 133
166 7 607 144 176 16 608 155 186 25 609 135 136 41 610 153 150 57
611 133 102 71 612 144 117 91 613 94 94 94 614 94 94 94 615 133 70
103 616 155 90 121 617 133 38 135 618 155 58 153 619 133 6 167 620
144 16 176 621 155 26 185 622 101 6 199 623 112 16 208 624 123 26
217 625 101 38 167 626 123 58 185 627 101 70 135 628 123 90 153 629
101 102 103 630 123 122 121 631 101 134 71 632 123 154 89 633 101
166 39 634 123 186 57 635 101 198 7 636 112 208 16 637 123 218 25
638 69 230 7 639 68 253 3 640 84 252 3 641 80 240 16 642 91 250 25
643 71 200 41 644 89 214 57 645 69 166 71 646 92 169 91 647 99 99
99 648 99 99 99 649 69 134 103 650 91 154 121 651 69 102 135 652 91
122 153 653 69 70 167 654 91 90 185 655 69 38 199 656 91 58 217 657
69 6 231 658 68 3 253 659 85 3 253 660 80 16 240 661 91 26 249 662
37 38 231 663 48 48 240 664 59 58 249 665 37 70 199 666 59 90 217
667 37 102 167 668 59 122 185 669 37 134 135 670 59 154 153 671 37
166 103 672 59 186 121 673 37 198 71 674 57 218 85 675 37 230 39
676 48 240 48 677 52 247 58 678 4 231 70 679 3 253 68 680 21 224 87
681 104 104 104 682 104 104 104 683 16 240 80 684 27 250 89 685 5
198 103 686 16 208 112 687 27 218 121 688 5 166 135 689 16 176 144
690 27 186 153 691 5 134 167 692 16 144 176 693 27 154 185 694 5
102 199 695 16 112 208 696 27 122 217 697 5 70 231 698 3 68 253 699
3 85 253 700 16 80 240 701 27 90 249 702 5 102 231 703 3 102 253
704 3 119 253 705 16 112 240 706 27 122 249 707 5 134 199 708 16
144 208 709 27 154 217 710 5 166 167 711 17 177 177 712 25 186 181
713 5 198 135 714 31 187 135 715 109 109 109 716 109 109 109 717 27
218 153 718 5 230 103 719 3 253 102 720 3 253 119 721 16 240 112
722 27 250 121 723 37 230 71 724 48 240 80 725 59 250 89 726 37 198
103 727 59 218 121 728 37 166 135 729 59 186 153 730 37 134 167 731
59 154 185 732 37 102 199 733 59 122 217 734 37 70 231 735 48 80
240 736 59 90 249 737 69 38 231 738 80 48 240 739 91 58 249 740 69
70 199 741 91 90 217 742 70 103 168 743 91 122 185 744 69 134 135
745 88 155 146 746 70 167 104 747 91 186 121 748 74 179 76
749 114 114 114 750 114 114 114 751 91 218 89 752 69 230 39 753 80
240 48 754 91 250 57 755 101 230 7 756 102 253 3 757 119 253 3 758
112 240 16 759 123 250 25 760 101 198 39 761 123 218 57 762 101 166
71 763 123 186 89 764 101 134 103 765 123 154 121 766 101 102 135
767 123 122 153 768 101 70 167 769 123 90 185 770 101 38 199 771
123 58 217 772 101 6 231 773 102 3 253 774 119 3 253 775 112 16 240
776 123 24 245 777 133 6 199 778 144 16 208 779 152 27 210 780 134
39 168 781 155 58 185 782 126 75 128 783 120 120 120 784 120 120
120 785 155 90 153 786 133 102 103 787 155 122 121 788 133 134 71
789 155 154 89 790 133 166 39 791 155 186 57 792 133 198 7 793 144
208 16 794 155 218 25 795 165 166 7 796 176 176 16 797 187 186 25
798 165 134 39 799 187 154 57 800 165 102 71 801 187 122 89 802 165
70 103 803 187 90 121 804 165 38 135 805 187 58 153 806 165 6 167
807 176 16 176 808 187 26 185 809 197 6 135 810 208 16 144 811 219
26 153 812 197 38 103 813 216 59 114 814 198 71 72 815 219 90 89
816 178 101 50 817 125 125 125 818 125 125 125 819 219 122 57 820
197 134 7 821 208 144 16 822 219 154 25 823 229 102 7 824 253 102 3
825 253 119 3 826 240 112 16 827 251 122 25 828 229 70 39 829 240
80 48 830 251 90 57 831 229 38 71 832 240 48 80 833 251 58 89 834
229 6 103 835 253 3 102 836 253 3 119 837 240 16 112 838 251 26 121
839 229 6 135 840 253 3 136 841 253 3 153 842 240 16 144 843 251 26
153 844 229 38 103 845 240 48 112 846 251 58 121 847 230 71 72 848
240 80 80
849 251 90 89 850 204 101 50 851 130 130 130 852 130 130 130 853
240 112 48 854 251 122 57 855 229 134 7 856 253 136 3 857 253 153 3
858 240 144 16 859 251 154 25 860 197 166 7 861 208 176 16 862 219
186 25 863 197 134 39 864 219 154 57 865 197 102 71 866 219 122 89
867 197 70 103 868 219 90 121 869 197 38 135 870 219 58 153 871 197
6 167 872 208 16 176 873 219 26 185 874 165 6 199 875 176 16 208
876 187 26 217 877 165 38 167 878 185 58 181 879 165 70 135 880 187
90 153 881 167 104 105 882 185 122 117 883 165 134 71 884 170 143
91 885 135 135 135 886 135 135 135 887 165 166 39 888 187 186 57
889 165 198 7 890 176 208 16 891 187 218 25 892 133 230 7 893 136
253 3 894 153 253 3 895 144 240 16 896 155 250 25 897 133 198 39
898 155 218 57 899 133 166 71 900 155 186 89 901 133 134 103 902
155 154 121 903 133 102 135 904 155 122 153 905 133 70 167 906 155
90 185 907 133 38 199 908 155 58 217 909 133 6 231 910 136 3 253
911 153 3 253 912 144 16 240 913 155 26 249 914 101 38 231 915 113
49 241 916 121 58 245 917 101 70 199 918 118 91 195 919 141 141 141
920 141 141 141 921 101 102 167 922 123 122 185 923 101 134 135 924
123 154 153 925 101 166 103 926 123 186 121 927 101 198 71 928 123
218 89 929 101 230 39 930 112 240 48 931 123 250 57 932 69 230 71
933 80 240 80 934 91 250 89 935 69 198 103 936 91 218 121 937 69
166 135 938 91 186 153 939 69 134 167 940 91 154 185 941 69 102 199
942 91 122 217 943 69 70 231 944 80 80 240 945 91 90 249 946 37 102
231 947 48 112 240 948 59 122 249 949 39 136 201 950 57 154 213 951
42 171 171 952 66 169 169 953 146 146 146 954 146 146 146 955 37
198 135 956 59 218 153 957 37 230 103 958 48 240 112 959 59 250 121
960 5 230 135 961 3 253 136 962 3 253 153 963 16 240 144 964 27 250
153 965 5 198 167 966 16 208 176 967 27 218 185 968 5 166 199 969
16 176 208 970 27 186 217 971 5 134 231 972 3 136 253 973 3 153 253
974 16 144 240 975 27 154 249 976 5 166 231 977 3 170 253 978 3 187
253 979 16 176 240 980 25 186 245 981 5 198 199 982 18 209 209 983
24 219 210 984 4 231 167 985 3 253 174 986 21 224 170 987 151 151
151 988 151 151 151 989 16 240 176 990 27 250 185 991 37 230 135
992 48 240 144 993 59 250 153 994 37 198 167 995 59 218 185 996 37
166 199 997 59 186 217 998 37 134 231 999 48 144 240 1000 59 154
249 1001 69 102 231 1002 80 112 240 1003 91 122 249 1004 69 134 199
1005 91 154 217 1006 69 166 167 1007 91 186 185 1008 69 198 135
1009 91 218 153 1010 69 230 103 1011 80 240 112 1012 91 250 121
1013 102 231 72 1014 112 240 80 1015 123 250 89 1016 105 201 106
1017 120 211 122 1018 108 167 129 1019 123 173 150 1020 106 127 149
1021 156 156 156 1022 156 156 156 1023 123 154 185 1024 101 102 199
1025 123 122 217 1026 101 70 231 1027 112 80 240 1028 123 90 249
1029 133 38 231 1030 144 48 240 1031 155 58 249 1032 133 70 199
1033 155 90 217 1034 133 102 167 1035 155 122 185 1036 133 134 135
1037 155 154 153 1038 133 166 103 1039 155 186 121 1040 133 198 71
1041 155 218 89 1042 133 230 39 1043 144 240 48 1044 155 248 53
1045 165 230 7 1046 170 253 3 1047 185 251 4 1048 176 240 16 1049
187 250 25 1050 169 201 42 1051 184 211 58 1052 166 167 72 1053 181
173 92 1054 152 127 102 1055 161 161 161 1056 161 161 161 1057 187
154 121 1058 165 102 135 1059 187 122 153 1060 165 70 167 1061 187
90 185 1062 165 38 199 1063 187 58 217 1064 165 6 231 1065 170 3
253 1066 187 3 253 1067 176 16 240 1068 187 26 249 1069 197 6 199
1070 208 16 208 1071 219 26 217 1072 197 38 167 1073 219 58 185
1074 197 70 135 1075 219 90 153 1076 197 102 103 1077 219 122 121
1078 198 135 72 1079 219 154 89 1080 197 166 39 1081 216 187 50
1082 197 198 7 1083 208 208 16 1084 220 208 21 1085 232 166 6 1086
253 171 3 1087 249 184 6 1088 213 161 31 1089 167 167 167 1090 167
167 167 1091 251 186 25 1092 229 134 39 1093 240 144 48 1094 251
154 57 1095 229 102 71 1096 240 112 80 1097 251 122 89 1098 229 70
103 1099 240 80 112
1100 251 90 121 1101 229 38 135 1102 240 48 144 1103 251 58 153
1104 229 6 167 1105 253 3 170 1106 253 3 187 1107 240 16 176 1108
251 26 185 1109 229 6 199 1110 253 3 204 1111 253 3 221 1112 240 16
208 1113 251 26 217 1114 229 38 167 1115 241 49 177 1116 249 58 181
1117 229 70 135 1118 242 81 145 1119 248 91 146 1120 229 102 103
1121 242 114 114 1122 215 100 136 1123 172 172 172 1124 172 172 172
1125 229 134 71 1126 240 144 80 1127 251 154 89 1128 229 166 39
1129 240 176 48 1130 251 186 57 1131 229 198 7 1132 253 204 3 1133
253 221 3 1134 240 208 16 1135 251 218 25 1136 197 230 7 1137 204
253 3 1138 221 253 3 1139 208 240 16 1140 219 250 25 1141 197 198
39 1142 219 218 57 1143 197 166 71 1144 219 186 89 1145 197 134 103
1146 217 150 121 1147 197 102 135 1148 219 122 153 1149 199 72 169
1150 217 86 185 1151 197 38 199 1152 214 48 219 1153 197 5 233 1154
205 3 253 1155 217 6 249 1156 187 31 213 1157 177 177 177 1158 177
177 177 1159 219 26 249 1160 165 38 231 1161 176 48 240 1162 187 58
249 1163 165 70 199 1164 187 90 217 1165 165 102 167 1166 187 122
185 1167 165 134 135 1168 187 154 153 1169 165 166 103 1170 187 186
121 1171 165 198 71 1172 187 218 89 1173 165 230 39 1174 176 240 48
1175 187 250 57 1176 133 230 71 1177 144 240 80 1178 155 250 89
1179 133 198 103 1180 142 209 132 1181 124 167 145 1182 145 186 162
1183 126 142 172 1184 144 157 188 1185 123 114 195 1186 140 125 215
1187 126 88 227 1188 130 95 236 1189 127 109 240 1190 92 113 205
1191 182 182 182 1192 182 182 182 1193 112 112 240 1194 123 122 249
1195 101 134 199 1196 123 154 217 1197 101 166 167 1198 123 186 185
1199 101 198 135 1200 123 218 153 1201 101 230 103 1202 112 240 112
1203 123 250 121 1204 69 230 135 1205 80 240 144 1206 91 250 153
1207 69 198 167 1208 91 218 185 1209 69 166 199 1210 91 186 217
1211 69 134 231 1212 80 144 240 1213 91 154 249 1214 37 166 231
1215 48 176 240 1216 59 186 249 1217 39 200 201 1218 57 218 213
1219 37 230 167 1220 50 241 177 1221 52 247 186 1222 4 231 199 1223
3 253 208 1224 21 224 198 1225 187 187 187 1226 187 187 187 1227 16
240 208 1228 27 250 217 1229 5 198 231 1230 3 204 253 1231 3 221
253 1232 16 208 240 1233 27 218 249 1234 5 230 231 1235 3 253 238
1236 3 238 253 1237 2 241 241 1238 12 241 241 1239 2 251 241 1240
12 251 241 1241 2 241 251 1242 12 241 251 1243 2 251 251 1244 0 253
253 1245 3 255 253 1246 3 253 255 1247 12 251 251 1248 16 240 240
1249 17 253 253 1250 27 250 249 1251 38 231 200 1252 48 240 208
1253 59 250 217 1254 39 199 232 1255 49 209 241 1256 59 214 247
1257 71 168 233 1258 83 161 213 1259 193 193 193 1260 193 193 193
1261 91 186 249 1262 69 198 199 1263 91 218 217 1264 69 230 167
1265 80 240 176 1266 91 250 185 1267 101 230 135 1268 112 240 144
1269 123 250 153 1270 101 198 167 1271 123 218 185 1272 101 166 199
1273 123 186 217 1274 101 134 231 1275 112 144 240 1276 123 154 249
1277 133 102 231 1278 144 112 240 1279 155 122 249 1280 133 134 199
1281 155 154 217 1282 134 167 168 1283 155 186 185 1284 145 204 115
1285 163 223 127 1286 150 234 93 1287 161 238 91 1288 175 245 89
1289 180 235 58 1290 189 240 64 1291 194 238 74 1292 165 188 86
1293 198 198 198 1294 198 198 198 1295 187 218 121 1296 165 166 135
1297 187 186 153 1298 165 134 167 1299 187 154 185 1300 165 102 199
1301 187 122 217 1302 165 70 231 1303 176 80 240 1304 187 90 249
1305 197 38 231 1306 208 48 240 1307 219 58 249 1308 197 70 199
1309 219 90 217 1310 197 102 167 1311 219 122 185 1312 197 134 135
1313 219 154 153 1314 197 166 103 1315 219 186 121 1316 198 199 72
1317 219 218 89 1318 197 230 39 1319 209 241 49 1320 219 248 53
1321 229 230 7 1322 250 240 3 1323 238 251 2 1324 241 241 2 1325
248 243 2 1326 214 222 20 1327 203 203 203 1328 203 203 203 1329
251 251 2 1330 253 253 0 1331 255 253 3 1332 253 255 3 1333 241 241
12 1334 251 241 12 1335 241 251 12 1336 251 251 12 1337 240 240 16
1338 253 253 17 1339 251 250 25 1340 229 198 39 1341 240 208 48
1342 251 218 57 1343 229 153 87 1344 241 161 97 1345 249 172 104
1346 231 125 118 1347 241 135 125 1348 248 145 128 1349 230 99 142
1350 241 110 151
1351 248 120 154 1352 230 74 167 1353 242 85 177 1354 247 91 180
1355 230 48 193 1356 242 60 203 1357 246 63 207 1358 231 22 219
1359 248 21 228 1360 211 37 209 1361 208 208 208 1362 208 208 208
1363 241 2 241 1364 251 2 241 1365 241 12 241 1366 251 12 241 1367
241 2 251 1368 251 2 251 1369 253 0 253 1370 255 3 253 1371 253 3
255 1372 241 12 251 1373 251 12 251 1374 240 16 240 1375 253 17 253
1376 251 26 249 1377 229 38 231 1378 253 34 253 1379 240 48 240
1380 253 51 253 1381 251 58 249 1382 229 70 199 1383 240 80 208
1384 249 90 213 1385 229 102 167 1386 240 112 176 1387 224 127 185
1388 216 140 159 1389 217 150 150 1390 227 165 153 1391 211 177 114
1392 224 189 123 1393 222 202 107 1394 191 189 86 1395 213 213 213
1396 213 213 213 1397 240 208 80 1398 251 218 89 1399 229 230 39
1400 253 253 34 1401 240 240 48 1402 253 253 51 1403 251 250 57
1404 197 230 71 1405 208 240 80 1406 219 250 89 1407 197 198 103
1408 219 218 121 1409 197 166 135 1410 219 186 153 1411 197 134 167
1412 219 154 185 1413 197 102 199 1414 219 122 217 1415 197 70 231
1416 208 80 240 1417 219 90 249 1418 165 102 231 1419 176 112 240
1420 187 122 249 1421 167 136 201 1422 185 154 213 1423 165 166 167
1424 182 188 175 1425 167 200 137 1426 185 218 149 1427 167 232 105
1428 161 213 109 1429 219 219 219 1430 219 219 219 1431 187 250 121
1432 133 230 135 1433 144 240 144 1434 155 250 153 1435 133 198 167
1436 155 218 185 1437 133 166 199 1438 155 186 217 1439 133 134 231
1440 144 144 240 1441 155 154 249 1442 101 166 231 1443 112 176 240
1444 123 186 249 1445 101 198 199 1446 127 222 208 1447 111 234 170
1448 122 238 167 1449 133 248 176 1450 92 234 189 1451 97 231 199
1452 108 240 211 1453 88 191 224 1454 101 203 235 1455 100 202 243
1456 64 214 234 1457 64 233 252 1458 78 214 240 1459 83 224 250
1460 92 220 241 1461 95 216 229 1462 98 208 218 1463 224 224 224
1464 224 224 224 1465 80 240 240 1466 85 253 253 1467 91 250 249
1468 101 230 199 1469 112 240 208 1470 123 250 217 1471 101 198 231
1472 112 208 240 1473 123 218 249 1474 133 166 231 1475 144 176 240
1476 155 186 249 1477 133 198 199 1478 155 218 217 1479 133 230 167
1480 144 240 176 1481 155 250 185 1482 165 230 135 1483 176 240 144
1484 187 250 153 1485 165 198 167 1486 185 214 185 1487 165 166 199
1488 187 186 217 1489 166 135 232 1490 206 114 245 1491 211 117 244
1492 220 96 240 1493 224 104 243 1494 221 116 235 1495 221 125 222
1496 203 130 202 1497 229 229 229 1498 229 229 229 1499 197 166 167
1500 219 186 185 1501 197 198 135 1502 219 218 153 1503 197 230 103
1504 208 240 112 1505 221 242 126 1506 231 225 82 1507 250 247 74
1508 240 236 86 1509 252 249 91 1510 248 248 90 1511 231 203 102
1512 240 211 112 1513 251 221 120 1514 231 174 133 1515 235 181 143
1516 246 191 152 1517 228 145 165 1518 235 149 175 1519 247 160 185
1520 226 109 199 1521 237 119 208 1522 242 114 220 1523 229 77 234
1524 248 77 251 1525 235 89 242 1526 245 95 251 1527 241 101 246
1528 230 112 234 1529 242 116 245 1530 207 119 207 1531 234 234 234
1532 234 234 234 1533 253 119 253 1534 251 122 249 1535 229 134 199
1536 240 144 208 1537 251 154 217 1538 229 166 167 1539 240 176 176
1540 251 186 185 1541 229 198 135 1542 240 208 144 1543 251 218 153
1544 229 230 103 1545 253 253 102 1546 240 240 112 1547 253 253 119
1548 251 250 121 1549 184 236 169 1550 191 243 176 1551 202 244 166
1552 190 210 179 1553 206 221 196 1554 188 176 209 1555 206 192 223
1556 196 157 236 1557 206 151 238 1558 213 161 245 1559 181 174 234
1560 184 185 229 1561 193 197 233 1562 180 212 194 1563 190 227 196
1564 165 210 158 1565 239 239 239 1566 239 239 239 1567 176 240 176
1568 187 250 185 1569 133 230 199 1570 144 240 208 1571 155 250 217
1572 133 198 231 1573 144 208 240 1574 155 218 249 1575 101 230 231
1576 102 253 253 1577 112 240 240 1578 119 253 253 1579 123 250 249
1580 133 230 231 1581 136 253 253 1582 144 240 240 1583 155 250 249
1584 153 253 253 1585 165 230 199 1586 176 240 208 1587 184 243 218
1588 165 198 231 1589 176 208 240 1590 188 208 245 1591 198 167 232
1592 208 176 240 1593 213 189 236 1594 226 226 193 1595 231 234 199
1596 200 233 185 1597 210 242 194 1598 196 221 182 1599 245 245 245
1600 245 245 245 1601 229 230 135
1602 253 253 136 1603 240 240 144 1604 251 250 153 1605 253 253 153
1606 229 198 167 1607 240 208 176 1608 238 225 198 1609 222 178 205
1610 232 191 217 1611 242 196 221 1612 227 157 234 1613 246 159 253
1614 237 161 231 1615 251 173 240 1616 250 170 244 1617 233 182 228
1618 252 186 246 1619 237 180 238 1620 251 189 249 1621 248 192 245
1622 233 202 209 1623 242 210 217 1624 244 223 212 1625 236 236 181
1626 252 249 186 1627 241 243 192 1628 249 248 196 1629 245 248 199
1630 209 235 209 1631 217 244 216 1632 201 222 198 1633 250 250 250
1634 250 250 250 1635 197 198 231 1636 208 208 240 1637 219 218 249
1638 165 230 231 1639 170 253 253 1640 176 240 240 1641 187 250 249
1642 187 253 253 1643 197 230 231 1644 204 253 253 1645 208 240 240
1646 219 250 249 1647 221 253 253 1648 229 230 199 1649 253 253 204
1650 240 240 208 1651 251 250 217 1652 251 249 221 1653 137 118 138
1654 151 122 151 1655 144 125 144 1656 150 130 149 1657 151 132 151
1658 140 140 139 1659 151 150 143 1660 151 143 151 1661 143 149 149
1662 144 144 144 1663 145 144 144 1664 148 146 144 1665 146 150 144
1666 141 141 136 1667 244 244 244 1668 244 244 244 1669 231 231 240
1670 240 231 240 1671 231 240 240 1672 240 240 239 1673 240 240 240
1674 244 242 242 1675 242 244 242 1676 242 242 244
______________________________________
______________________________________ APPENDIX C Dbase.rgb:
transparency precursor data Patch # R G B
______________________________________ 1 0 0 0 2 6 0 2 3 5 3 6 4 7
1 4 5 7 3 4 6 0 4 4 7 2 4 8 8 10 4 4 9 2 1 1 10 12 7 4 11 2 7 4 12
10 5 3 13 4 1 2 14 10 8 6 15 23 0 4 16 7 7 4 17 5 6 3 18 16 4 7 19
23 1 3 20 34 4 0 21 36 4 7 22 56 8 6 23 51 7 4 24 56 4 7 25 12 38 7
26 16 42 8 27 17 78 4 28 22 41 4 29 26 40 7 30 17 4 12 31 18 8 16
32 15 4 29 33 20 8 21 34 26 4 29 35 5 5 5 36 1 5 4 37 3 7 59 38 4 4
65 39 2 1 93 40 10 1 70 41 19 4 86 42 5 22 9 43 13 29 17 44 20 32
22 45 7 82 3 46 8 85 3 47 8 116 3 48 11 91 3 49 15 99 7 50 38 18 8
51 51 20 4 52 55 28 4 53 35 7 16 54 44 1 27 55 55 7 32 56 60 3 2 57
62 1 3 58 77 2 3 59 74 7 4 60 84 3 3 61 100 6 5 62 100 1 6 63 123 1
7 64 113 6 4 65 124 5 1 66 62 7 0 67 69 15 1 68 79 24 1 69 10 10 10
70 7 10 5 71 62 7 13 72 72 4 20 73 83 4 28 74 26 4 63 75 41 5 70 76
50 5 84 77 28 7 14 78 45 20 23 79 36 63 0 80 43 73 7 81 49 84 1 82
10 157 5 83 11 154 4 84 15 181 8 85 11 153 4 86 14 161 5 87 7 71 7
88 10 73 11 89 14 81 18 90 7 10 49 91 12 16 60 92 17 17 78 93 7 1
128 94 11 0 130 95 13 4 163 96 18 4 149 97 22 4 160 98 13 8 180 99
0 4 255 100 10 1 161 101 14 1 178 102 17 7 171 103 16 16 16 104 15
15 10 105 1 1 111 106 7 0 121 107 15 2 130 108 5 60 42 109 9 67 52
110 14 74 67 111 8 131 10 112 10 136 13 113 12 144 16 114 36 221 37
115 54 223 50 116 23 203 19 117 32 217 31 118 153 237 134 119 38
113 5 120 60 114 6 121 53 129 4 122 26 43 8 123 49 64 17 124 29 2
46 125 47 13 75 126 24 4 120 127 43 5 132 128 56 4 149 129 63 4 63
130 75 0 71 131 87 5 83 132 63 4 11 133 83 16 21 134 61 48 2 135 69
61 1 136 79 69 3 137 21 21 21 138 22 20 16 139 92 9 3 140 102 13 7
141 113 19 1 142 96 8 8 143 108 8 26 144 119 4 35 145 138 3 4 146
146 0 4 147 180 3 4 148 151 4 5 149 162 2 4 150 195 4 4 151 199 5 7
152 197 0 6 153 201 0 4 154 209 4 4 155 129 3 6 156 139 12 6 157
156 13 4 158 137 1 8 159 148 5 28 160 160 2 36 161 95 3 54 162 109
2 80 163 121 5 92 164 97 7 8 165 115 27 21 166 94 58 6 167 107 63 1
168 112 69 3 169 59 98 7 170 75 105 7 171 26 26 26 172 29 24 22 173
82 120 2 174 56 35 7 175 79 63 17 176 56 0 49 177 79 7 73 178 54 4
125 179 68 8 134 180 82 4 150 181 24 1 177 182 33 2 174 183 43 4
177 184 28 2 104 185 51 4 124 186 25 36 47 187 50 55 66 188 25 97
10 189 39 120 19 190 18 172 8 191 34 199 13 192 55 217 29 193 53
223 52 194 36 221 36 195 18 195 13 196 42 220 36 197 22 200 14 198
51 221 43 199 154 238 133 200 96 230 82 201 14 120 48 202 14 119 55
203 14 124 56 204 7 45 93 205 31 31 31 206 35 29 28 207 5 62 101
208 13 68 113 209 4 8 170 210 9 3 182 211 15 9 195 212 5 8 171 213
7 1 162 214 10 7 170 215 11 5 182 216 19 3 177 217 13 4 170 218 14
5 168 219 18 4 170 220 21 7 174 221 27 4 181 222 6 1 180 223 12 3
186 224 17 6 173 225 6 13 169 226 10 31 169 227 11 48 177 228 9 102
89 229 12 112 97 230 17 119 112 231 21 199 31 232 24 209 51 233 37
221 67 234 35 220 31 235 24 205 17 236 34 215 31 237 26 209 24 238
23 200 17 239 36 36 36 240 40 35 34 241 90 229 81 242 17 198 15 243
27 214 30 244 152 238 132 245 106 231 81 246 48 215 25
247 16 171 9 248 27 211 27 249 21 90 36 250 36 110 61 251 26 23 90
252 52 51 116 253 25 4 172 254 49 7 183 255 29 5 173 256 38 6 175
257 55 5 183 258 53 7 177 259 63 4 183 260 79 4 187 261 63 4 100
262 85 4 121 263 59 30 44 264 83 60 63 265 67 89 5 266 93 112 17
267 65 157 1 268 84 168 4 269 91 186 6 270 97 96 7 271 110 103 1
272 118 115 4 273 42 42 42 274 44 41 39 275 89 35 5 276 113 62 13
277 91 6 44 278 114 2 70 279 88 4 116 280 106 3 133 281 118 4 147
282 136 2 57 283 148 1 85 284 160 2 96 285 130 6 12 286 155 1 27
287 129 46 4 288 140 60 0 289 154 71 5 290 179 1 1 291 190 1 4 292
203 3 1 293 189 3 5 294 199 4 28 295 212 4 39 296 198 1 6 297 193 3
0 298 198 1 5 299 199 4 4 300 211 5 3 301 204 7 1 302 203 4 8 303
204 3 6 304 197 5 5 305 203 2 1 306 202 3 0 307 47 47 47 308 49 47
45 309 199 5 4 310 199 5 4 311 203 5 4 312 228 7 2 313 255 1 6 314
203 0 0 315 207 23 21 316 206 4 4 317 208 7 6 318 213 6 3 319 214 5
6 320 199 0 3 321 208 1 8 322 216 10 0 323 202 1 4 324 213 3 44 325
215 4 40 326 177 4 85 327 189 0 91 328 207 7 97 329 172 1 5 330 198
4 22 331 173 53 4 332 183 64 7 333 192 73 2 334 128 92 3 335 141
104 3 336 153 115 0 337 128 32 11 338 147 63 18 339 124 4 50 340
147 0 72 341 52 52 52 342 55 52 51 343 123 5 129 344 143 3 142 345
157 6 155 346 89 2 179 347 104 7 189 348 120 1 187 349 94 8 101 350
115 2 129 351 86 28 42 352 113 52 62 353 92 89 5 354 116 111 18 355
93 147 1 356 111 155 1 357 121 166 3 358 101 229 62 359 94 221 28
360 79 200 11 361 52 148 5 362 78 172 13 363 60 83 34 364 85 105 61
365 58 33 84 366 81 59 111 367 61 6 170 368 84 4 190 369 62 8 180
370 68 7 193 371 90 1 183 372 38 1 172 373 52 5 177 374 64 2 182
375 57 57 57 376 61 58 57 377 22 7 173 378 38 4 186 379 22 12 145
380 45 40 165 381 19 83 83 382 38 102 111 383 12 151 25 384 18 179
33 385 17 191 14 386 56 224 57 387 92 228 82 388 24 198 17 389 45
221 44 390 28 215 33 391 18 194 16 392 92 230 82 393 18 194 16 394
51 223 51 395 29 215 31 396 58 225 56 397 25 209 26 398 18 197 15
399 31 218 32 400 61 225 57 401 24 206 21 402 26 209 25 403 62 225
58 404 26 209 25 405 25 206 24 406 19 191 14 407 19 191 15 408 19
191 15 409 62 62 62 410 67 63 63 411 38 222 42 412 22 209 38 413 16
201 33 414 24 217 50 415 5 167 96 416 6 177 104 417 7 188 116 418 6
92 141 419 0 101 146 420 6 107 159 421 7 15 195 422 3 16 193 423 14
24 204 424 6 0 176 425 10 1 169 426 20 1 175 427 18 7 170 428 18 5
168 429 18 7 172 430 23 3 168 431 17 3 174 432 22 1 168 433 22 3
173 434 25 5 168 435 22 6 173 436 25 0 175 437 30 1 182 438 22 5
173 439 32 2 189 440 34 1 171 441 21 4 171 442 28 1 180 443 68 68
68 444 73 70 70 445 30 5 176 446 5 6 167 447 14 7 179 448 11 0 182
449 17 5 181 450 25 1 190 451 4 2 187 452 11 1 178 453 20 11 194
454 7 90 206 455 1 92 209 456 3 95 203 457 4 157 136 458 4 161 143
459 3 171 154 460 59 224 105 461 30 218 103 462 23 212 92 463 34
221 45 464 17 200 33 465 19 201 24 466 19 201 17 467 54 223 50 468
24 208 23 469 26 212 26 470 94 230 81 471 61 225 56 472 34 219 31
473 33 219 31 474 92 230 81 475 29 216 30 476 28 212 30 477 73 73
73 478 79 77 77 479 15 190 12 480 55 225 57 481 17 198 16 482 11
141 81 483 24 163 101 484 26 73 128 485 47 95 150 486 33 40 213 487
47 10 198 488 28 4 173 489 56 4 179 490 57 8 211 491 55 4 190 492
79 7 182 493 65 6 175 494 85 6 190 495 81 4 182 496 109 7 189 497
125 2 184
498 55 7 175 499 84 1 198 500 60 9 143 501 83 31 166 502 63 74 84
503 89 99 113 504 51 135 21 505 50 159 28 506 156 238 132 507 65
206 12 508 63 221 37 509 60 207 15 510 35 217 31 511 78 78 78 512
85 83 83 513 102 205 12 514 124 228 37 515 127 227 32 516 97 131 6
517 123 151 14 518 94 76 38 519 119 98 68 520 94 13 89 521 114 35
117 522 97 3 172 523 120 5 192 524 101 7 186 525 112 7 188 526 133
7 189 527 138 1 191 528 152 3 200 529 167 1 193 530 130 7 109 531
152 2 130 532 126 17 45 533 151 54 60 534 130 88 6 535 153 110 15
536 132 141 8 537 147 152 2 538 160 164 1 539 164 95 1 540 178 105
7 541 191 117 7 542 166 26 6 543 183 60 14 544 164 0 47 545 83 83
83 546 91 90 90 547 194 7 79 548 172 4 139 549 185 1 143 550 202 4
154 551 215 5 88 552 214 5 92 553 216 2 95 554 213 5 9 555 221 4 26
556 217 32 3 557 224 45 2 558 227 61 2 559 211 7 2 560 205 4 4 561
214 1 5 562 220 8 10 563 224 18 10 564 216 1 26 565 216 1 22 566
210 6 52 567 219 4 46 568 218 1 55 569 217 5 94 570 216 6 92 571
206 4 121 572 214 1 83 573 215 1 106 574 222 12 13 575 219 22 29
576 223 19 43 577 219 28 4 578 213 31 4 579 88 88 88 580 98 97 97
581 218 73 1 582 215 52 4 583 214 82 2 584 208 87 4 585 220 102 4
586 230 113 1 587 211 19 11 588 230 54 21 589 217 1 59 590 219 6 86
591 212 5 146 592 212 3 146 593 210 0 153 594 176 3 193 595 189 3
188 596 201 2 201 597 166 0 117 598 193 1 134 599 163 17 44 600 180
60 65 601 163 87 4 602 181 110 15 603 168 147 4 604 180 150 0 605
190 161 1 606 129 193 9 607 147 214 18 608 159 229 32 609 130 132 5
610 151 152 16 611 120 79 29 612 143 98 57 613 94 94 94 614 104 103
104 615 122 11 89 616 146 42 115 617 124 4 172 618 151 6 190 619
151 6 184 620 156 4 189 621 160 4 191 622 140 7 189 623 192 7 185
624 173 8 189 625 90 1 182 626 115 3 190 627 91 3 141 628 114 19
166 629 88 69 89 630 115 95 117 631 98 122 40 632 119 145 58 633 94
204 17 634 139 235 80 635 87 208 17 636 101 206 15 637 127 233 78
638 43 220 36 639 23 194 13 640 75 226 65 641 75 226 65 642 26 209
21 643 71 225 56 644 24 197 14 645 57 223 55 646 19 189 14 647 99
99 99 648 110 109 110 649 36 126 76 650 45 155 93 651 56 74 132 652
81 91 149 653 53 3 196 654 79 19 211 655 64 7 188 656 96 4 193 657
98 0 177 658 113 6 192 659 157 4 193 660 125 4 184 661 156 4 195
662 35 5 171 663 54 1 186 664 73 1 195 665 27 6 180 666 62 7 208
667 17 63 193 668 39 86 210 669 17 129 132 670 37 148 146 671 92
230 115 672 93 230 117 673 33 219 35 674 33 219 34 675 55 224 52
676 20 198 16 677 50 222 44 678 47 222 44 679 28 213 29 680 23 202
21 681 104 104 104 682 115 115 116 683 25 212 28 684 88 230 79 685
89 230 92 686 57 224 87 687 17 197 33 688 85 232 146 689 84 233 157
690 20 211 140 691 1 151 185 692 0 153 196 693 0 161 208 694 0 62
203 695 7 65 205 696 16 91 214 697 13 13 200 698 14 22 207 699 17
83 215 700 16 28 204 701 20 54 211 702 7 82 211 703 8 116 206 704
10 160 205 705 14 149 210 706 28 133 211 707 6 128 207 708 7 131
214 709 5 141 203 710 28 221 171 711 85 236 187 712 11 205 189 713
30 217 87 714 20 206 99 715 109 109 109 716 120 120 122 717 65 228
130 718 54 224 53 719 89 230 79 720 26 214 29 721 26 214 29 722 19
203 20 723 27 214 30 724 28 215 30 725 23 204 24 726 28 217 53 727
36 220 57 728 20 209 128 729 54 228 148 730 11 122 177 731 29 141
201 732 35 37 213 733 47 75 217 734 37 1 194 735 48 15 205 736 56
30 207 737 87 1 184 738 116 4 194 739 130 6 201 740 62 1 186 741 97
13 214 742 61 51 183 743 84 78 203 744 64 114 127 745 87 133 147
746 24 198 58 747 53 221 88 748 19 186 13
749 114 114 114 750 126 125 127 751 55 223 54 752 69 226 65 753 17
187 12 754 28 213 29 755 29 213 29 756 70 226 65 757 70 226 64 758
92 229 81 759 29 210 25 760 108 229 50 761 105 213 20 762 70 188 22
763 101 220 39 764 96 119 89 765 119 139 118 766 92 61 132 767 117
85 152 768 93 4 199 769 115 14 216 770 110 5 181 771 133 3 189 772
186 4 190 773 207 5 185 774 217 3 200 775 213 1 185 776 198 2 193
777 161 2 189 778 144 4 181 779 156 2 185 780 134 1 198 781 151 7
177 782 123 5 141 783 120 120 120 784 131 131 133 785 147 18 162
786 124 66 85 787 144 96 112 788 128 122 39 789 150 142 66 790 131
183 7 791 154 219 24 792 133 204 12 793 148 204 12 794 160 224 27
795 173 181 6 796 183 202 10 797 192 220 18 798 163 128 4 799 188
149 14 800 159 76 37 801 180 96 65 802 159 6 105 803 178 36 116 804
171 4 177 805 193 3 189 806 175 3 191 807 188 6 181 808 200 0 182
809 212 4 179 810 215 7 192 811 215 7 179 812 214 8 115 813 213 0
132 814 206 8 46 815 228 41 66 816 194 81 6 817 125 125 125 818 137
136 138 819 226 105 9 820 205 137 7 821 217 145 6 822 230 157 4 823
225 90 1 824 230 117 4 825 225 153 7 826 229 109 2 827 228 117 4
828 217 34 8 829 228 56 21 830 233 73 27 831 218 6 53 832 221 5 72
833 210 7 91 834 208 1 147 835 213 5 164 836 214 4 220 837 205 4
147 838 207 7 176 839 204 4 188 840 216 4 187 841 214 7 179 842 222
2 219 843 214 3 194 844 213 0 116 845 206 3 128 846 216 8 142 847
213 7 52 848 215 27 68
849 229 40 56 850 216 79 4 851 130 130 130 852 142 141 143 853 230
95 5 854 226 106 11 855 217 138 6 856 237 148 4 857 220 160 1 858
219 147 2 859 219 155 2 860 207 184 4 861 213 207 8 862 230 221 15
863 202 133 4 864 223 153 9 865 197 76 34 866 225 97 57 867 204 4
97 868 226 30 115 869 214 1 175 870 217 3 188 871 215 2 188 872 206
5 191 873 215 8 181 874 174 1 194 875 185 7 189 876 198 4 180 877
174 3 193 878 192 1 185 879 161 1 145 880 182 18 165 881 157 71 87
882 176 94 110 883 153 113 35 884 175 135 65 885 135 135 135 886
148 148 149 887 162 173 7 888 185 207 15 889 171 218 19 890 180 226
23 891 188 211 11 892 89 214 19 893 90 226 52 894 159 206 12 895
157 233 43 896 163 234 42 897 148 236 77 898 138 207 16 899 127 170
25 900 145 203 33 902 148 137 123 903 123 56 135 904 146 84 152 905
122 6 200 906 148 12 217 907 143 5 184 908 149 4 187 909 174 7 180
910 170 4 183 911 153 6 183 912 138 1 196 913 149 4 190 914 158 2
198 915 200 7 193 916 168 4 185 917 89 0 189 918 106 17 204 919 141
141 141 920 153 154 155 921 89 44 181 922 114 77 200 923 95 112 127
924 118 131 145 925 38 175 43 926 75 201 81 927 93 228 63 928 52
215 28 929 40 221 38 930 105 231 81 931 34 203 19 932 34 220 39 933
44 221 46 934 34 219 43 935 44 221 53 936 54 223 79 937 30 174 118
938 31 210 145 939 57 107 173 940 81 127 198 941 54 26 201 942 77
68 209 943 83 1 189 944 101 16 212 945 103 25 210 946 31 56 210 947
34 81 214 948 62 93 207 949 17 111 215 950 14 135 216 951 8 190 164
952 33 227 187 953 146 146 146 954 159 160 161 955 23 210 100 956
11 202 127 957 23 206 26 958 55 224 54 959 40 223 45 960 13 198 47
961 23 211 49 962 52 223 114 963 29 217 99 964 28 217 114 965 25
221 159 966 24 222 166 967 10 202 171 968 4 193 221 969 8 206 206
970 21 226 226 971 3 122 206 972 7 142 216 973 2 140 206 974 6 120
214 975 6 133 214 976 5 169 205 977 1 174 218 978 17 222 217 979 4
178 211 980 10 203 208 981 64 237 227 982 19 215 226 983 13 209 213
984 69 229 144 985 35 220 123 986 16 206 145 987 151 151 151 988
163 165 166 989 11 199 136 990 30 223 158 991 13 199 57 992 12 201
118 993 41 223 126 994 8 196 148 995 9 200 175 996 7 180 223 997 6
199 213 998 19 103 210 999 13 106 209 1000 24 120 215 1001 65 36
201 1002 62 60 211 1003 104 75 218 1004 50 100 217 1005 84 117 218
1006 31 166 165 1007 22 198 189 1008 60 225 114 1009 24 210 124
1010 93 230 85 1011 28 209 43 1012 23 190 28 1013 97 230 82 1014 59
219 36 1015 48 215 32 1016 97 230 89 1017 30 202 32 1018 79 163 120
1019 124 175 146 1020 98 100 164 1021 156 156 156 1022 168 170 171
1023 118 121 191 1024 91 26 206 1025 110 52 203 1026 111 6 190 1027
106 12 211 1028 124 15 206 1029 154 2 196 1030 129 8 198 1031 139 4
192 1032 127 4 196 1033 145 9 207 1034 127 39 184 1035 149 75 200
1036 132 110 132 1037 152 129 150 1038 124 158 75 1039 150 185 114
1040 111 212 23 1041 144 235 78 1042 113 228 48 1043 140 231 47
1044 131 223 29 1045 181 241 75 1046 179 227 26 1047 196 223 21
1048 178 236 43 1049 195 243 75 1050 197 245 131 1051 189 233 32
1052 170 169 28 1053 191 189 39 1054 159 115 85 1055 161 161 161
1056 173 175 176 1057 179 129 108 1058 156 56 128 1059 176 76 149
1060 159 1 197 1061 186 7 217 1062 168 1 186 1063 189 5 190 1064
170 8 184 1065 174 0 190 1066 196 3 187 1067 181 7 188 1068 192 2
196 1069 214 4 188 1070 216 3 179 1071 211 7 179 1072 210 4 182
1073 216 0 187 1074 203 8 146 1075 225 14 159 1076 190 67 87 1077
220 86 109 1078 194 116 35 1079 221 136 63 1080 201 173 10 1081 225
202 12 1082 205 207 11 1083 218 246 74 1084 228 230 24 1085 245 192
6 1086 244 193 6 1087 248 230 25 1088 235 199 7 1089 167 167 167
1090 178 180 182 1091 231 209 10 1092 235 123 3 1093 216 138 6 1094
218 146 6 1095 234 71 37 1096 233 90 49 1097 226 103 54 1098 222 4
100 1099 224 32 105 1100 215 47 112
1101 217 1 173 1102 205 5 181 1103 218 7 184 1104 208 8 200 1105
218 2 191 1106 208 4 189 1107 204 1 188 1108 208 5 194 1109 216 6
189 1110 209 4 197 1111 211 3 187 1112 213 6 189 1113 204 4 189
1114 220 7 201 1115 213 4 186 1116 215 7 188 1117 218 6 144 1118
222 9 151 1119 216 17 163 1120 228 68 94 1121 219 80 96 1122 221 83
109 1123 172 172 172 1124 183 185 187 1125 234 115 30 1126 240 124
43 1127 238 133 58 1128 237 165 3 1129 246 178 5 1130 245 190 15
1131 240 252 121 1132 232 238 39 1133 244 221 16 1134 249 246 53
1135 226 229 23 1136 205 244 72 1137 212 210 12 1138 232 208 11
1139 210 224 20 1140 226 224 19 1141 199 240 48 1142 223 206 10
1143 196 163 25 1144 221 186 36 1145 190 111 83 1146 214 125 111
1147 191 50 133 1148 222 71 151 1149 206 2 202 1150 226 9 217 1151
210 4 187 1152 212 5 193 1153 255 6 255 1154 216 7 198 1155 205 7
187 1156 214 3 191 1157 177 177 177 1158 188 190 193 1159 213 6 181
1160 159 6 188 1161 168 8 187 1162 180 2 185 1163 160 7 192 1164
183 5 197 1165 158 48 182 1166 175 72 198 1167 153 113 130 1168 178
127 148 1169 161 159 95 1170 187 177 114 1171 168 238 60 1172 166
206 16 1173 162 226 32 1174 168 221 28 1175 179 211 21 1176 97 223
42 1177 76 202 23 1178 110 230 66 1179 104 229 73 1180 94 206 36
1181 133 149 135 1182 159 175 154 1183 129 104 169 1184 150 125 194
1185 122 36 203 1186 142 63 207 1187 136 1 192 1188 127 12 205 1189
132 22 208 1190 97 55 219 1191 182 182 182 1192 193 194 198 1193 95
46 210 1194 135 98 225 1195 89 95 219 1196 108 111 215 1197 83 149
163 1198 108 172 186 1199 151 240 162 1200 66 209 123 1201 20 189
21 1202 29 217 40 1203 94 230 88 1204 91 230 112 1205 23 207 111
1206 47 222 115 1207 48 228 157 1208 83 236 185 1209 28 157 218
1210 47 176 227 1211 46 95 214 1212 54 102 216 1213 94 104 206 1214
3 154 209 1215 3 167 214 1216 6 184 217 1217 62 237 215 1218 23 225
207 1219 39 224 145 1220 16 205 166 1221 49 229 172 1222 17 215 193
1223 15 207 177 1224 47 233 215 1225 187 187 187 1226 198 199 203
1227 7 201 195 1228 7 201 211 1229 14 216 215 1230 17 222 218 1231
57 236 226 1232 44 233 214 1233 18 222 208 1234 17 222 219 1235 38
230 212 1236 18 224 222 1237 24 227 218 1238 48 234 228 1239 10 204
221 1240 43 232 228 1241 43 232 228 1242 18 217 223 1243 34 229 225
1244 11 207 216 1245 11 204 220 1246 12 207 216 1247 47 233 221
1248 12 207 209 1249 14 211 217 1250 0 228 255 1251 24 224 198 1252
30 229 218 1253 52 236 224 1254 83 238 226 1255 15 208 210 1256 16
212 217 1257 16 146 208 1258 31 150 214 1259 193 193 193 1260 202
204 209 1261 50 155 217 1262 144 243 215 1263 78 238 230 1264 82
232 161 1265 12 197 150 1266 82 234 170 1267 98 230 117 1268 26 203
67 1269 77 227 108 1270 48 225 158 1271 50 223 177 1272 100 136 214
1273 121 169 233 1274 97 87 222 1275 120 82 216 1276 160 102 214
1277 121 30 201 1278 127 35 205 1279 138 70 211 1280 127 91 218
1281 150 116 218 1282 134 143 163 1283 155 172 186 1284 106 219 101
1285 135 213 133 1286 43 207 27 1287 0 210 30 1288 104 229 66 1289
160 232 41 1290 160 208 17 1291 173 233 45 1292 149 219 48 1293 198
198 198 1294 207 208 214 1295 175 210 43 1296 161 147 133 1297 182
166 146 1298 156 97 167 1299 175 115 187 1300 158 24 199 1301 182
53 207 1302 152 5 193 1303 164 8 212 1304 175 15 216 1305 205 1 178
1306 212 4 190 1307 221 4 209 1308 204 4 204 1309 222 2 197 1310
196 26 180 1311 222 55 199 1312 192 101 125 1313 217 119 143 1314
194 149 89 1315 219 169 108 1316 199 231 35 1317 223 222 20 1318
199 227 28 1319 208 206 15 1320 219 209 16 1321 241 239 44 1322 221
233 33 1323 253 218 17 1324 232 209 16 1325 233 246 75 1326 219 236
45 1327 203 203 203 1328 212 213 220 1329 216 237 42 1330 245 202
10 1331 234 240 44 1332 228 235 34 1333 248 240 44 1334 235 222 19
1335 242 221 19 1336 224 215 17 1337 245 227 24 1338 218 205 14
1339 218 216 19 1340 238 238 43 1341 244 253 123 1342 236 204 15
1343 234 159 27 1344 241 164 61 1345 234 170 124 1346 233 105 87
1347 239 112 101 1348 226 112 140 1349 233 46 129 1350 233 65 137
1351 235 69 143
1352 219 8 198 1353 220 7 202 1354 221 9 213 1355 206 2 193 1356
215 4 186 1357 212 8 183 1358 208 3 193 1359 212 2 187 1360 215 1
180 1361 208 208 208 1362 216 218 225 1363 212 0 179 1364 203 3 188
1365 211 6 187 1366 216 4 185 1367 211 7 187 1368 203 4 186 1369
214 8 196 1370 216 6 191 1371 216 4 191 1372 215 1 190 1373 207 6
190 1374 213 7 187 1375 217 4 190 1376 214 7 181 1377 216 8 186
1378 213 4 178 1379 215 5 193 1380 216 8 191 1381 213 6 179 1382
220 2 203 1383 207 1 189 1384 220 1 204 1385 228 25 178 1386 219 43
189 1387 226 58 199 1388 230 97 127 1389 238 106 133 1390 238 110
145 1391 230 147 102 1392 238 155 141 1393 226 166 112 1394 232 216
19 1395 213 213 213 1396 221 223 231 1397 243 235 38 1398 250 249
78 1399 233 243 54 1400 221 204 9 1401 241 240 42 1402 234 210 14
1403 234 203 12 1404 188 203 17 1405 196 236 43 1406 208 227 27
1407 195 207 54 1408 216 243 74 1409 192 143 128 1410 215 164 145
1411 188 91 167 1412 212 115 187 1413 194 27 214 1414 224 54 204
1415 192 1 195 1416 203 3 198 1417 216 8 209 1418 149 33 212 1419
161 49 221 1420 172 72 206 1421 154 103 216 1422 178 116 224 1423
161 146 168 1424 183 166 188 1425 165 202 126 1426 178 237 130 1427
125 230 61 1428 134 215 32 1429 219 219 219 1430 226 228 236 1431
174 239 77 1432 51 219 61 1433 64 220 65 1434 81 208 72 1435 117
201 158 1436 127 238 176 1437 123 135 209 1438 151 164 230 1439 119
71 204 1440 125 83 206 1441 149 111 220 1442 108 122 210 1443 148
133 208 1444 149 159 216 1445 32 210 202 1446 88 238 225 1447 57
226 151 1448 89 234 164 1449 41 218 154 1450 83 235 204 1451 62 233
216 1452 18 203 214 1453 21 216 223 1454 49 228 207 1455 148 243
231 1456 21 213 206 1457 85 238 231 1458 29 221 224 1459 24 217 222
1460 28 220 214 1461 29 221 225 1462 46 229 220 1463 224 224 224
1464 231 233 242 1465 21 216 214 1466 18 212 222 1467 22 220 224
1468 79 234 201 1469 22 218 204 1470 36 226 208 1471 58 184 224
1472 107 188 215 1473 115 237 232 1474 122 122 205 1475 132 137 214
1476 168 160 227 1477 125 187 201 1478 145 229 224 1479 87 213 137
1480 105 233 161 1481 82 218 152 1482 140 223 58 1483 169 220 74
1484 178 227 95 1485 171 195 162 1486 193 228 179 1487 162 136 207
1488 186 157 224 1489 158 76 218 1490 171 95 222 1491 189 106 207
1492 194 11 215 1493 210 19 212 1494 214 49 209 1495 193 84 216
1496 216 105 220 1497 229 229 229 1498 236 238 247 1499 184 130 160
1500 209 154 182 1501 191 187 129 1502 216 217 146 1503 171 234 55
1504 188 229 34 1505 202 218 25 1506 231 237 42 1507 248 249 72
1508 240 227 25 1509 229 211 16 1510 250 245 52 1511 234 198 58
1512 242 212 84 1513 255 231 92 1514 227 136 124 1515 234 146 135
1516 238 150 144 1517 230 88 166 1518 235 99 174 1519 224 114 187
1520 212 33 224 1521 225 38 210 1522 218 53 222 1523 213 4 189 1524
218 2 198 1525 218 5 197 1526 210 7 201 1527 222 1 198 1528 228 20
215 1529 220 37 224 1530 207 33 202 1531 234 234 234 1532 241 244
253 1533 227 51 200 1534 229 55 219 1535 228 80 215 1536 236 95 222
1537 227 124 233 1538 222 129 157 1539 232 143 164 1540 244 154 173
1541 226 184 127 1542 238 196 153 1543 215 220 121 1544 227 246 72
1545 253 225 23 1546 237 238 50 1547 255 255 0 1548 244 206 27 1549
188 223 75 1550 194 223 70 1551 198 213 97 1552 191 185 158 1553
216 210 177 1554 189 128 202 1555 214 153 227 1556 192 85 225 1557
204 97 226 1558 213 105 227 1559 166 130 218 1560 183 142 219 1561
201 160 232 1562 168 193 202 1563 195 217 218 1564 139 217 139 1565
239 239 239 1566 255 249 254 1567 140 224 138 1568 177 208 146 1569
89 235 195 1570 36 217 193 1571 110 237 211 1572 110 173 224 1573
135 185 214 1574 129 211 219 1575 20 202 221 1576 35 221 225 1577
23 210 223 1578 44 225 217 1579 25 200 212 1580 70 220 227 1581 75
216 214 1582 89 225 226 1583 111 214 220 1584 116 226 221 1585 116
205 185 1586 154 214 199 1587 176 228 214 1588 170 173 219 1589 187
183 223 1590 206 210 226 1591 194 130 218 1592 206 144 222 1593 218
154 206 1594 198 180 200 1595 219 210 214 1596 186 211 126 1597 200
229 145 1598 220 213 160 1599 245 245 245 1600 253 251 255 1601 223
237 60 1602 253 223 45
1603 239 214 63 1604 215 207 80 1605 242 209 83 1606 224 179 157
1607 238 191 168 1608 252 204 173 1609 222 127 198 1610 235 144 214
1611 215 158 228 1612 227 66 213 1613 229 31 208 1614 235 89 200
1615 237 97 201 1616 233 95 215 1617 230 125 223 1618 235 114 216
1619 237 141 227 1620 240 146 228 1621 238 141 222 1622 227 172 198
1623 239 188 206 1624 250 197 218 1625 229 240 155 1626 235 248 148
1627 241 242 164 1628 232 237 171 1629 231 229 175 1630 204 240 193
1631 215 250 199 1632 229 216 211 1633 250 250 250 1634 254 253 255
1635 195 168 219 1636 206 180 224 1637 212 192 221 1638 183 248 230
1639 159 235 235 1640 170 231 228 1641 205 216 217 1642 208 241 211
1643 197 236 211 1644 208 207 225 1645 215 253 231 1646 218 206 224
1647 217 226 203 1648 226 231 189 1649 238 235 195 1650 236 243 199
1651 250 201 211 1652 251 201 217 1653 227 165 224 1654 239 157 219
1655 237 173 228 1656 249 184 234 1657 249 186 229 1658 231 223 240
1659 254 236 223 1660 253 228 201 1661 238 247 238 1662 238 242 211
1663 241 245 210 1664 253 239 207 1665 236 247 210 1666 250 203 217
1667 255 255 255 1668 255 255 255 1669 240 240 209 1670 254 236 207
1671 239 245 221 1672 240 206 235 1673 230 247 238 1674 213 251 234
1675 230 251 223 1676 233 218 236
______________________________________
______________________________________ APPENDIX D
______________________________________ * Input Layer : 3 Neurons
fully connected to Hidden layer * Hidden Layer : 14 Neurons fully
connected to Output layer * Output Layer : 3 Neurons * 1 Bias
Neuron fully connected to Hidden and Output ** Input .fwdarw.
Hidden weights ** * Input 1 Input 2 Input 3 Bias -0.442736586
-0.623409628 0.925939232 -1.318630255 0.390761213 -0.523850528
-0.794199828 0.389915371 -0.062237680 0.900454106 -0.609265760
0.638924552 -0.251614215 -0.869924483 0.507059054 -1.193555639
0.589267421 1.247208658 -0.201817678 -0.242378778 0.872374815
0.742210042 -0.308714505 -0.354207446 -0.133642721 1.398686683
0.549923172 -0.520948811 0.975541146 -0.402403146 1.048848840
-0.400613982 -0.912802945 0.638310392 -0.283297317 -0.404199663
-0.792644223 -0.121435503 -0.565998492 0.419756745 -0.346402606
-1.252863484 1.827742432 -0.083786462 0.405769046 -1.296117015
-0.518716257 0.337546105 1.798235531 -0.608837188 -0.163968699
0.016968235 0.964840914 -1.269434779 0.945630648 -0.675165394 **
Hidden .fwdarw. output weights ** * Output 1 Output 2 Output 3
0.571908169 0.221515675 1.007163353 0.268681112 -0.278919924
-1.027308743 -0.884099627 0.823127289 0.000674341 -1.005828712
0.426739593 0.763209790 0.639980075 1.076764081 -0.479292934
0.961454034 0.879561628 0.101335486 -0.353316065 1.552545259
0.760079152 0.870425982 -0.210038559 1.168321013 -1.410277006
0.086453719 0.601415216 -0.713774215 -0.885393597 -1.095775013
-1.121825306 -1.242603117 1.726716248 -0.559382966 -1.614395371
-1.113117723 1.767996710 -1.013364897 -0.478047840 0.931748193
-0.834048414 1.094327453 -0.976110925 -0.167233221 -0.881178242
.rarw. Bias ______________________________________
______________________________________ APPENDIX E Patch # R G B
______________________________________ 1 12 11 10 2 14 11 11 3 13
12 12 4 14 11 11 5 14 12 11 6 12 13 11 7 12 12 13 8 15 12 11 9 12
11 10 10 16 13 11 11 12 14 11 12 15 12 11 13 13 11 11 14 15 14 11
15 22 10 11 16 14 13 11 17 13 13 11 18 18 11 12 19 22 10 11 20 30
11 9 21 31 11 11 22 50 11 11 23 45 11 10 24 50 10 11 25 16 36 11 26
18 40 11 27 18 104 10 28 21 38 10 29 23 36 10 30 18 11 14 31 19 12
15 32 17 10 22 33 20 12 17 34 23 10 21 35 13 13 11 36 12 13 11 37
12 10 48 38 13 9 56 39 12 7 100 40 15 8 63 41 20 8 87 42 13 22 12
43 16 26 14 44 19 27 16 45 14 116 10 46 14 123 10 47 14 186 11 48
15 135 10 49 17 151 11 50 32 17 11 51 44 17 10 52 49 22 9 53 30 11
15 54 37 8 20 55 49 9 23 56 55 10 10 57 58 9 10 58 78 9 10 59 74 10
10 60 89 9 10 61 114 9 11 62 114 8 12 63 150 8 13 64 135 9 11 65
152 9 10 66 58 11 9 67 67 14 9 68 81 19 9 69 15 14 13 70 14 15 11
71 57 10 13 72 71 9 16 73 87 8 21 74 23 8 52 75 35 7 61 76 44 7 83
77 25 12 14 78 38 16 17 79 30 70 8 80 35 87 10 81 41 110 8 82 14
231 13 83 14 229 12 84 15 242 15 85 14 228 12 86 15 233 13 87 14 91
11 88 15 94 12 89 16 110 14 90 13 12 37 91 15 14 47 92 18 13 71 93
16 7 161 94 18 6 164 95 22 7 207 96 23 7 191 97 27 6 204 98 23 8
222 99 27 9 248 100 20 6 205 101 25 6 220 102 25 7 215 103 18 16 15
104 17 17 12 105 13 7 132 106 16 6 150 107 20 6 164 108 12 64 27
109 13 74 35 110 15 84 49 111 13 208 13 112 14 213 14 113 14 221 15
114 22 250 27 115 34 250 32 116 17 247 19 117 20 249 24 118 176 247
115 119 30 174 10 120 51 170 10 121 42 197 10 122 23 40 11 123 41
66 13 124 25 8 34 125 40 9 67 126 24 7 147 127 41 6 167 128 59 5
191 129 59 7 52 130 76 5 64 131 94 6 82 132 59 9 13 133 87 13 16
134 55 42 8 135 65 60 8 136 79 72 8 137 20 19 16 138 21 18 14 139
101 11 10 140 118 12 11 141 135 15 9 142 108 10 12 143 127 9 20 144
145 7 26 145 171 8 12 146 181 7 12 147 213 8 14 148 187 8 13 149
198 8 13 150 222 9 14 151 224 9 16 152 223 7 16 153 225 8 15 154
229 9 15 155 159 8 12 156 173 11 12 157 192 11 12 158 170 8 13 159
184 7 23 160 196 6 30 161 106 6 43 162 130 5 79 163 149 5 100 164
109 10 12 165 139 17 16 166 104 51 9 167 125 57 8 168 132 66 8 169
51 138 10 170 71 148 10 171 23 21 18 172 25 20 16 173 79 176 9 174
50 28 10 175 79 59 12 176 50 7 37 177 81 7 65 178 52 5 156 179 71 6
170 180 96 4 193 181 32 6 219 182 39 6 217 183 49 6 219 184 26 6
119 185 49 6 154 186 22 27 31 187 41 42 47 188 22 144 11 189 30 186
14 190 16 238 14 191 22 246 17 192 35 249 22 193 34 250 33 194 22
250 26 195 15 246 17 196 26 249 26 197 17 247 17 198 32 249 29 199
177 248 114 200 85 249 54 201 15 188 30 202 15 185 35 203 15 193 36
204 13 33 93 205 26 24 20 206 29 22 19 207 11 56 105 208 14 62 126
209 17 8 214 210 22 7 223 211 26 8 231 212 18 8 215 213 19 6 206
214 20 8 214 215 23 7 223 216 27 6 219 217 23 7 214 218 23 7 212
219 26 7 214 220 28 7 217 221 34 6 222 222 20 7 222 223 24 7 226
224 25 7 216 225 18 10 213 226 18 17 212 227 17 30 219 228 12 143
78 229 13 162 89 230 15 171 114 231 16 247 23 232 17 248 33 233 23
250 44 234 22 250 24 235 17 248 19 236 22 249 24 237 18 248 21 238
17 247 18 239 29 27 23 240 33 26 22 241 76 249 53 242 15 246 18 243
18 249 24 244 174 248 112 245 100 249 52 246 30 249 21 247 15 238
14
248 18 249 22 249 19 126 22 250 27 162 39 251 23 14 90 252 43 30
132 253 31 6 215 254 56 6 223 255 34 6 216 256 43 6 218 257 64 5
223 258 60 6 219 259 75 5 223 260 100 4 226 261 61 6 111 262 95 5
150 263 52 19 28 264 85 45 42 265 61 116 9 266 98 158 12 267 52 225
10 268 75 231 11 269 81 239 12 270 106 123 9 271 126 135 8 272 138
158 9 273 34 32 26 274 36 31 24 275 96 25 9 276 135 53 11 277 100 7
32 278 137 5 64 279 99 5 141 280 130 4 170 281 150 4 190 282 169 5
49 283 184 4 91 284 196 4 111 285 161 9 14 286 191 6 24 287 159 33
9 288 174 49 8 289 190 64 9 290 212 8 13 291 219 8 14 292 226 9 14
293 219 8 14 294 224 7 27 295 230 7 36 296 223 8 16 297 221 9 13
298 223 8 15 299 224 9 15 300 230 9 15 301 227 10 13 302 226 8 16
303 227 8 16 304 223 9 15 305 226 8 14 306 225 9 13 307 38 36 29
308 40 36 28 309 224 9 14 310 224 9 14 311 226 9 15 312 236 10 15
313 242 8 19 314 226 8 14 315 229 14 20 316 227 9 15 317 228 9 15
318 230 9 15 319 231 9 16 320 224 8 15 321 228 8 17 322 232 11 13
323 225 8 15 324 230 6 41 325 231 7 38 326 210 5 93 327 217 4 105
328 226 5 114 329 207 8 14 330 224 8 23 331 208 38 10 332 215 51 11
333 220 64 10 334 156 108 8 335 172 131 9 336 185 151 8 337 158 21
12 338 184 50 13 339 152 6 40 340 182 5 71 341 43 41 33 342 46 40
32 343 155 4 164 344 181 4 184 345 195 4 199 346 114 4 220 347 138
4 227 348 160 3 225 349 107 6 113 350 143 4 165 351 91 17 27 352
135 32 42 353 98 109 9 354 136 150 12 355 92 212 9 356 119 217 10
357 133 225 10 358 91 249 38 359 79 248 21 360 62 244 15 361 39 220
11 362 66 234 13 363 52 99 19 364 86 137 36 365 51 18 76 366 81 36
119 367 69 5 213 368 108 4 227 369 72 6 221 370 84 5 229 371 116 4
223 372 43 5 215 373 59 5 219 374 77 5 223 375 48 46 37 376 53 47
37 377 28 7 216 378 45 6 226 379 24 9 186 380 41 19 208 381 17 98
70 382 27 129 113 383 14 227 19 384 16 241 23 385 15 245 17 386 36
250 36 387 79 249 54 388 18 246 18 389 28 250 29 390 19 249 25 391
15 246 18 392 78 249 54 393 15 246 18 394 32 250 33 395 19 249 24
396 38 250 36 397 18 248 22 398 15 246 18 399 20 249 24 400 40 250
36 401 17 248 20 402 18 248 21 403 41 250 37 404 18 248 21 405 18
248 21 406 16 245 17 407 16 245 17 408 16 245 17 409 54 52 41 410
61 52 42 411 23 250 29 412 16 248 27 413 14 247 24 414 17 249 33
415 10 233 80 416 11 238 91 417 11 241 107 418 11 107 172 419 9 127
179 420 11 135 196 421 21 11 231 422 18 11 230 423 24 14 235 424 20
6 219 425 21 6 213 426 28 6 218 427 25 7 214 428 25 7 212 429 26 7
215 430 29 6 212 431 26 6 217 432 29 6 212 433 29 6 216 434 30 6
212 435 29 7 216 436 32 5 218 437 37 5 223 438 29 7 216 439 40 6
227 440 39 5 215 441 28 6 215 442 35 6 222 443 62 59 47 444 69 61
49 445 36 6 219 446 18 8 211 447 24 8 221 448 23 6 223 449 26 7 222
450 35 6 228 451 20 7 226 452 23 6 220 453 29 8 230 454 14 91 235
455 12 97 236 456 12 103 233 457 9 220 150 458 9 223 161 459 9 229
175 460 39 249 81 461 19 249 81 462 16 248 68 463 21 250 30 464 15
247 24 465 15 247 21 466 15 247 18 467 34 250 32 468 17 248 21 469
18 249 22 470 81 249 53 471 40 250 35 472 21 249 24 473 21 249 24
474 78 249 53 475 19 249 24 476 19 249 23 477 68 66 53 478 77 72 57
479 14 245 16 480 35 250 36 481 15 246 18 482 13 213 62 483 17 229
86 484 20 65 152 485 35 99 183 486 37 20 239 487 56 7 232 488 34 6
216 489 65 5 221 490 73 6 238 491 66 5 228 492 98 5 223 493 76 5
218 494 109 5 227 495 102 4 223 496 145 4 226 497 165 3 223 498 62
6 218
499 111 4 232 500 62 6 183 501 95 11 209 502 54 68 69 503 90 106
114 504 40 206 15 505 37 229 18 506 180 247 112 507 45 246 16 508
42 249 25 509 40 247 17 510 22 249 24 511 75 74 58 512 86 81 65 513
94 245 15 514 126 248 25 515 130 248 23 516 101 191 10 517 141 212
12 518 103 76 21 519 144 111 43 520 105 7 90 521 138 13 137 522 124
4 215 523 160 4 228 524 132 4 225 525 149 4 226 526 175 4 226 527
181 3 227 528 195 3 231 529 206 3 227 530 162 5 130 531 189 4 167
532 156 10 32 533 189 32 42 534 159 99 9 535 188 140 12 536 156 198
10 537 173 209 10 538 186 219 10 539 198 108 9 540 210 125 10 541
218 147 11 542 202 17 12 543 216 45 13 544 200 5 41 545 83 81 65
546 95 93 74 547 221 5 83 548 206 4 180 549 215 3 185 550 223 3 197
551 230 5 100 552 229 5 107 553 230 4 113 554 230 9 17 555 233 7 27
556 232 20 13 557 235 30 12 558 236 45 11 559 230 10 14 560 227 9
15 561 231 8 16 562 233 10 18 563 235 13 17 564 231 7 27 565 232 7
25 566 229 6 49 567 232 6 44 568 232 5 54 569 230 5 110 570 230 5
107 571 225 4 155 572 229 4 94 573 229 4 132 574 234 11 19 575 233
13 26 576 234 11 37 577 233 18 13 578 231 20 13 579 90 90 71 580
107 105 84 581 232 62 10 582 232 36 12 583 231 77 10 584 228 86 11
585 232 113 11 586 235 132 11 587 230 13 16 588 237 35 19 589 231 5
59 590 231 5 97 591 227 4 188 592 227 3 188 593 226 3 196 594 211 3
227 595 218 3 224 596 224 3 230 597 201 3 148 598 219 3 174 599 200
10 34 600 215 36 48 601 198 92 9 602 213 135 13 603 197 200 10 604
206 201 10 605 212 212 11 606 139 239 13 607 162 245 17 608 176 247
23 609 154 186 10 610 180 209 13 611 146 79 16 612 179 109 33 613
100 100 80 614 116 115 96 615 150 6 93 616 182 16 133 617 162 4 215
618 193 4 226 619 192 4 223 620 197 3 225 621 200 3 226 622 183 4
226 623 219 4 222 624 209 4 225 625 116 4 222 626 154 4 227 627 108
4 181 628 145 6 209 629 92 52 77 630 136 90 122 631 106 174 21 632
139 204 32 633 82 245 16 634 154 249 51 635 71 246 17 636 92 245 16
637 135 249 50 638 26 249 26 639 17 245 17 640 55 249 41 641 55 249
41 642 18 248 20 643 51 249 35 644 18 246 17 645 37 249 35 646 16
244 17 647 108 108 87 648 126 125 105 649 26 189 54 650 31 222 73
651 46 59 157 652 78 81 181 653 65 5 231 654 102 8 237 655 77 5 227
656 127 4 229 657 127 4 219 658 151 4 228 659 198 3 228 660 165 4
223 661 198 3 229 662 39 6 214 663 65 5 225 664 94 4 230 665 34 7
222 666 80 6 236 667 20 45 229 668 34 74 237 669 14 184 149 670 24
205 166 671 79 249 91 672 80 249 94 673 21 249 26 674 21 249 25 675
35 250 33 676 16 246 18 677 31 250 29 678 29 250 29 679 19 249 23
680 17 247 20 681 116 117 95 682 133 136 115 683 17 249 23 684 72
249 51 685 74 249 64 686 37 249 60 687 15 246 24 688 67 248 138 689
64 248 155 690 14 246 139 691 9 205 216 692 8 205 224 693 8 211 230
694 13 48 234 695 16 50 235 696 18 90 238 697 25 9 233 698 25 13
237 699 20 75 239 700 25 15 235 701 25 34 238 702 15 76 237 703 12
143 233 704 11 210 229 705 13 195 233 706 20 168 235 707 11 165 233
708 12 169 236 709 10 187 230 710 16 246 182 711 63 247 195 712 10
241 208 713 19 249 62 714 15 247 78 715 124 126 103 716 142 144 125
717 43 249 115 718 34 250 34 719 74 249 51 720 18 249 23 721 18 249
23 722 15 247 20 723 18 249 24 724 19 249 24 725 17 247 21 726 19
249 35 727 23 249 37 728 14 246 120 729 32 248 144 730 12 160 213
731 20 183 229 732 40 18 239 733 44 53 240 734 47 5 230 735 58 8
235 736 64 13 236 737 112 4 224 -738 156 4 229 739 174 4 232 740 76
4 225 741 132 6 238 742 61 25 223 743 92 49 233 744 51 144 139 745
82 171 169 746 18 246 37 747 34 249 61 748 16 243 16 749 132 134
111 750 151 151 133
751 35 250 34 752 49 250 41 753 15 244 16 754 19 249 23 755 19 249
23 756 50 250 41 757 50 250 40 758 79 249 53 759 19 248 21 760 101
249 31 761 97 246 18 762 54 242 17 763 91 248 25 764 102 158 68 765
139 184 113 766 100 34 158 767 140 60 186 768 124 4 232 769 158 5
238 770 145 4 221 771 175 3 226 772 217 3 225 773 226 3 221 774 229
3 229 775 228 3 221 776 222 3 226 777 201 3 225 778 186 3 221 779
197 3 223 780 178 3 231 781 192 4 218 782 156 4 182 783 142 144 121
784 156 161 143 785 186 6 205 786 152 44 71 787 180 87 112 788 156
167 21 789 185 194 39 790 145 235 12 791 171 245 19 792 143 243 15
793 164 242 15 794 177 246 21 795 197 230 12 796 203 239 15 797 208
244 18 798 195 173 10 799 214 200 13 800 197 66 21 801 215 96 43
802 195 5 126 803 212 12 137 804 207 3 218 805 220 3 224 806 211 3
226 807 217 4 220 808 223 3 220 809 227 3 217 810 229 4 225 811 228
4 217 812 229 5 144 813 228 3 171 814 228 7 41 815 236 19 57 816
222 77 11 817 149 152 129 818 166 168 150 819 234 117 13 820 224
180 12 821 229 189 12 822 233 202 12 823 234 90 10 824 235 140 11
825 231 199 13 826 235 125 11 827 234 140 11 828 233 21 14 829 237
37 18 830 238 57 20 831 232 6 50 832 232 5 76 833 228 5 104 834 226
3 190 835 228 3 206 836 229 3 236 837 225 4 189 838 226 4 216 839
225 3 223 840 229 3 222 841 228 4 217 842 231 3 236 843 228 3 226
844 228 4 148 845 225 4 165 846 229 4 183 847 230 7 49 848 232 12
62 849 237 19 46 850 232 71 11
851 157 160 137 852 173 174 158 853 236 98 12 854 235 119 13 855
229 179 12 856 235 190 12 857 228 207 12 858 229 192 11 859 228 202
12 860 220 228 13 861 221 239 15 862 228 242 19 863 223 174 11 864
231 199 13 865 225 63 22 866 236 94 38 867 225 4 115 868 234 10 138
869 228 3 215 870 229 3 223 871 228 3 223 872 225 3 225 873 229 4
219 874 210 3 228 875 216 4 225 876 222 3 219 877 210 3 227 878 219
3 222 879 198 3 188 880 214 5 207 881 195 47 74 882 212 78 110 883
189 144 19 884 210 178 39 885 164 167 145 886 180 183 166 887 187
226 12 888 204 241 16 889 190 244 18 890 197 246 20 891 205 241 16
892 73 247 18 893 75 249 32 894 178 242 15 895 174 248 28 896 181
248 28 897 166 249 49 898 150 243 16 899 145 228 16 900 165 242 21
901 155 146 80 902 182 172 122 903 151 25 165 904 182 54 186 905
164 4 232 906 193 5 238 907 185 4 223 908 191 3 225 909 209 4 220
910 207 3 222 911 194 4 222 912 182 3 230 913 191 3 226 914 200 3
230 915 223 4 226 916 206 3 223 917 117 4 227 918 142 6 234 919 172
175 154 920 186 190 174 921 104 17 221 922 141 42 232 923 99 130
138 924 136 160 165 925 26 239 26 926 60 245 53 927 79 249 39 928
33 249 22 929 25 250 27 930 99 249 52 931 22 247 19 932 21 250 27
933 27 250 30 934 21 249 29 935 27 249 34 936 35 249 53 937 20 234
111 938 19 245 147 939 44 116 210 940 74 144 228 941 62 11 234 942
84 28 236 943 107 4 227 944 137 6 237 945 137 8 237 946 32 34 237
947 31 66 238 948 56 79 235 949 17 129 238 950 14 174 237 951 10
237 183 952 18 246 200 953 178 181 161 954 192 196 181 955 16 247
78 956 11 245 121 957 17 248 22 958 35 250 34 959 25 250 30 960 13
246 31 961 17 249 32 962 32 249 93 963 19 249 76 964 18 248 96 965
15 247 165 966 15 247 175 967 10 241 189 968 9 232 233 969 9 239
222 970 13 243 231 971 11 156 233 972 11 186 236 973 10 186 232 974
12 150 237 975 11 172 236 976 9 218 228 977 9 221 234 978 12 243
227 979 9 224 230 980 10 238 224 981 37 245 229 982 12 240 233 983
11 239 226 984 47 248 137 985 21 248 108 986 13 244 149 987 184 187
168 988 195 200 187 989 11 243 137 990 17 247 163 991 13 247 37 992
12 245 107 993 24 248 112 994 10 241 158 995 10 240 195 996 10 224
236 997 9 236 228 998 18 113 236 999 15 121 235 1000 19 144 237
1001 74 14 233 1002 65 32 238 1003 128 40 239 1004 42 95 239 1005
84 118 238 1006 19 221 190 1007 14 238 210 1008 39 249 92 1009 16
246 113 1010 80 249 56 1011 19 248 29 1012 18 244 21 1013 86 249 54
1014 39 249 25 1015 30 249 23 1016 86 249 60 1017 20 247 23 1018 68
221 113 1019 141 222 153 1020 106 91 200 1021 189 192 175 1022 200
204 192 1023 137 122 223 1024 118 9 235 1025 140 19 234 1026 148 4
227 1027 145 5 237 1028 167 5 235 1029 196 3 229 1030 172 4 231
1031 182 4 228 1032 170 4 230 1033 190 4 234 1034 164 12 223 1035
188 35 231 1036 161 114 147 1037 186 145 173 1038 146 217 47 1039
181 231 95 1040 108 246 18 1041 161 249 50 1042 110 249 30 1043 152
248 30 1044 137 247 21 1045 203 248 49 1046 197 246 21 1047 211 244
20 1048 197 248 29 1049 214 248 49 1050 218 247 110 1051 205 247 24
1052 199 223 18 1053 215 233 24 1054 197 136 63 1055 194 197 181
1056 204 208 197 1057 214 155 98 1058 193 24 153 1059 211 40 183
1060 200 3 229 1061 218 4 237 1062 206 3 223 1063 218 3 225 1064
207 4 222 1065 210 3 225 1066 221 3 223 1067 214 4 224 1068 220 3
228 1069 228 3 223 1070 229 3 217 1071 227 4 218 1072 227 3 220
1073 229 3 222 1074 224 4 188 1075 232 5 201 1076 221 39 77 1077
234 59 112 1078 222 142 21 1079 234 172 41 1080 219 222 14 1081 228
236 17 1082 217 239 16 1083 226 248 50 1084 228 245 23 1085 235 230
15 1086 234 230 15 1087 235 244 24 1088 231 234 16 1089 199 202 188
1090 208 211 203 1091 229 238 17 1092 236 150 12 1093 229 179 12
1094 229 191 12 1095 239 52 26 1096 238 81 33 1097 236 106 35 1098
232 4 121 1099 234 11 121 1100 231 17 128 1101 229 3 213
1102 225 3 219 1103 229 4 220 1104 226 4 229 1105 229 3 224 1106
226 3 224 1107 224 3 223 1108 226 3 226 1109 229 3 223 1110 227 3
228 1111 227 3 222 1112 228 3 224 1113 225 3 224 1114 230 4 229
1115 228 3 222 1116 229 4 223 1117 230 4 185 1118 231 4 193 1119
229 5 205 1120 237 37 91 1121 234 53 91 1122 235 55 113 1123 203
206 193 1124 211 214 207 1125 238 134 21 1126 239 149 28 1127 239
164 38 1128 234 210 13 1129 236 220 14 1130 236 229 18 1131 236 247
98 1132 230 246 30 1133 233 242 20 1134 236 247 39 1135 227 244 22
1136 220 248 48 1137 221 240 17 1138 230 238 17 1139 219 244 20
1140 227 243 20 1141 214 248 32 1142 226 238 16 1143 219 214 18
1144 230 229 24 1145 222 122 63 1146 232 139 106 1147 220 18 163
1148 233 31 186 1149 226 3 230 1150 232 4 235 1151 227 3 222 1152
228 3 226 1153 238 4 243 1154 229 4 228 1155 225 4 223 1156 228 3
224 1157 207 209 198 1158 214 217 211 1159 228 4 219 1160 199 4 225
1161 206 4 224 1162 213 3 222 1163 201 4 227 1164 215 3 229 1165
197 15 221 1166 211 30 230 1167 189 117 142 1168 212 136 170 1169
196 210 71 1170 217 222 98 1171 189 248 38 1172 187 241 16 1173 180
247 23 1174 188 245 21 1175 199 242 18 1176 85 248 27 1177 59 245
18 1178 106 249 41 1179 97 249 46 1180 84 245 23 1181 159 192 141
1182 191 216 166 1183 157 89 205 1184 183 121 224 1185 161 11 234
1186 182 25 235 1187 179 3 228 1188 170 5 234 1189 176 7 235 1190
123 23 240 1191 211 213 202 1192 217 218 215 1193 120 17 237 1194
171 66 241 1195 98 73 239 1196 125 98 237 1197 73 194 189 1198 110
212 210 1199 171 247 157 1200 47 245 108 1201 16 244 19 1202 19 249
28 1203 82 249 59 1204 77 249 87 1205 16 246 94 1206 29 249 95 1207
28 248 159 1208 60 247 193 1209 19 202 236 1210 29 217 238 1211 39
87 238 1212 46 98 238 1213 102 90 234 1214 9 203 232 1215 9 215 233
1216 9 227 232 1217 35 246 222 1218 14 244 219 1219 22 248 142 1220
12 243 181 1221 27 247 180 1222 12 243 210 1223 12 242 195 1224 24
245 223 1225 214 215 206 1226 220 220 218 1227 9 239 215 1228 9 237
227 1229 11 241 226 1230 12 243 227 1231 31 245 229 1232 23 245 222
1233 12 244 221 1234 12 243 228 1235 20 245 222 1236 12 243 229
1237 14 244 226 1238 25 244 231 1239 10 237 232 1240 22 244 231
1241 22 244 231 1242 12 241 231 1243 18 244 230 1244 10 238 229
1245 10 237 231 1246 10 238 229 1247 24 245 227 1248 10 239 224
1249 11 240 228 1250 8 241 242 1251 14 245 212 1252 16 244 226 1253
27 245 228 1254 57 244 228 1255 11 239 225 1256 11 240 228 1257 14
192 132 1258 21 193 234 1259 217 219 211 1260 22 222 221 1261 33
195 235 1262 155 244 218 1263 51 244 231 1264 61 248 162 1265 11
241 160 1266 60 247 174 1267 88 249 94 1268 18 247 44 1269 58 249
83 1270 28 247 161 1271 28 246 189 1272 105 152 235 1273 133 194
240 1274 114 58 241 1275 151 46 238 1276 197 69 237 1277 160 9 233
1278 167 10 234 1279 177 31 237 1280 160 57 239 1281 185 96 238
1282 160 173 189 1283 184 205 209 1284 104 247 74 1285 154 243 120
1286 27 247 21 1287 10 249 25 1288 97 249 41 1289 178 248 27 1290
180 242 17 1291 193 247 29 1292 168 246 29 1293 220 221 214 1294
224 223 224 1295 199 242 27 1296 196 184 138 1297 213 204 155 1298
192 71 203 1299 209 97 220 1300 199 7 231 1301 216 16 234 1302 194
4 228 1303 205 4 236 1304 212 5 237 1305 225 3 217 1306 227 3 224
1307 231 3 232 1308 225 3 231 1309 231 3 227 1310 222 7 219 1311
232 16 229 1312 222 85 137 1313 233 113 164 1314 223 193 66 1315
233 211 92 1316 213 246 26 1317 226 243 20 1318 213 245 23 1319 220
239 17 1320 225 239 18 1321 233 246 33 1322 225 246 26 1323 236 240
21 1324 230 238 19 1325 232 247 52 1326 225 246 32 1327 223 223 217
1328 226 225 227 1329 223 247 30 1330 234 235 17 1331 231 246 32
1332 228 246 27 1333 235 246 33 1334 230 242 21 1335 233 242 21
1336 227 241 19 1337 234 243 23 1338 225 238 17 1339 224 242 19
1340 232 246 32 1341 237 247 101 1342 232 236 18 1343 236 205 20
1344 239 209 40 1345 238 208 118 1346 239 101 72 1347 240 110 93
1348 236 98 161 1349 236 15 158 1350 237 27 166 1351 237 30 175
1352 230 4 228
1353 230 4 230 1354 231 4 234 1355 225 3 226 1356 228 3 222 1357
228 4 220 1358 226 3 226 1359 227 3 222 1360 228 3 218 1361 225 225
220 1362 227 227 229 1363 227 3 217 1364 224 3 223 1365 227 3 222
1366 229 3 221 1367 227 4 223 1368 224 3 222 1369 228 4 227 1370
229 3 224 1371 229 3 224 1372 228 3 224 1373 226 3 224 1374 228 4
222 1375 229 3 224 1376 228 4 219 1377 229 4 222 1378 228 3 217
1379 229 3 226 1380 229 4 225 1381 228 4 217 1382 230 3 230 1383
226 3 224 1384 230 3 230 1385 233 6 216 1386 231 11 224 1387 234 18
229 1388 237 73 142 1389 239 87 151 1390 239 91 170 1391 237 181 87
1392 239 182 151 1393 236 206 99 1394 230 241 20 1395 227 226 222
1396 229 228 231 1397 234 245 30 1398 237 247 56 1399 231 247 38
1400 226 237 16 1401 233 246 32 1402 231 239 18 1403 231 236 17
1404 208 239 17 1405 212 247 30 1406 219 245 23 1407 217 241 33
1408 226 248 50 1409 222 173 131 1410 232 197 155 1411 218 56 204
1412 230 90 219 1413 222 7 236 1414 233 16 232 1415 220 3 227 1416
224 3 228 1417 229 4 233 1418 192 9 237 1419 203 15 240 1420 209 30
234 1421 191 71 237 1422 211 88 239 1423 195 170 195 1424 212 191
212 1425 196 238 111 1426 204 247 110 1427 131 249 37 1428 145 246
22 1429 229 228 225 1430 231 229 233 1431 197 248 50 1432 33 249 39
1433 44 249 41 1434 67 246 45 1435 123 237 165 1436 132 246 178
1437 144 144 233 1438 179 180 239 1439 150 34 234 1440 157 48 234
1441 185 86 239 1442 121 122 234 1443 180 133 232 1444 178 178 233
1445 18 240 218 1446 63 244 228 1447 35 248 150 1448 71 248 165
1449 23 246 158 1450 59 245 213 1451 36 245 223 1452 12 237 228
1453 13 241 231 1454 26 245 218 1455 159 242 229 1456 13 241 221
1457 59 244 231 1458 16 242 231 1459 14 241 230 1460 15 242 225
1461 16 242 231 1462 24 244 227 1463 231 230 227 1464 232 230 235
1465 13 241 226 1466 12 239 231 1467 13 242 231 1468 54 246 211
1469 13 243 218 1470 19 244 220 1471 37 222 235 1472 104 221 230
1473 105 242 231 1474 144 119 232 1475 158 144 235 1476 199 171 238
1477 136 220 220 1478 158 238 227 1479 73 245 129 1480 97 247 160
1481 64 245 152 1482 156 247 35 1483 195 245 47 1484 204 246 67
1485 201 229 172 1486 216 240 184 1487 196 136 231 1488 214 163 237
1489 198 34 239 1490 208 55 240 1491 219 72 233 1492 222 4 236 1493
228 5 234 1494 230 14 234 1495 221 40 237 1496 231 65 238 1497 232
231 229 1498 233 231 236 1499 216 136 188 1500 228 170 209 1501 219
227 120 1502 230 239 140 1503 192 248 35 1504 206 246 25 1505 216
243 21 1506 230 246 31 1507 237 247 51 1508 232 243 24 1509 229 239
19 1510 236 247 38 1511 235 235 38 1512 238 239 60 1513 240 244 69
1514 236 155 127 1515 238 169 144 1516 239 172 158 1517 236 48 202
1518 237 63 209 1519 234 87 219 1520 229 8 239 1521 233 9 234 1522
231 15 239 1523 228 3 223 1524 229 3 228 1525 230 3 227 1526 227 4
230 1527 231 3 228 1528 233 5 235 1529 232 9 239 1530 227 8 231
1531 233 232 231 1532 235 232 238 1533 234 14 229 1534 234 16 237
1535 234 34 236 1536 237 49 238 1537 234 92 241 1538 234 128 183
1539 237 152 190 1540 240 167 198 1541 235 222 119 1542 238 225 158
1543 230 242 102 1544 230 248 49 1545 236 242 23 1546 233 246 36
1547 232 247 19 1548 235 237 23 1549 212 245 48 1550 215 245 45
1551 221 241 70 1552 218 220 169 1553 230 231 187 1554 218 115 229
1555 229 149 238 1556 221 40 240 1557 226 54 240 1558 230 64 240
1559 200 119 237 1560 213 138 236 1561 223 162 240 1562 196 219 219
1563 216 229 225 1564 159 243 128 1565 235 233 232 1566 238 233 237
1567 160 245 125 1568 206 237 142 1569 68 246 204 1570 19 243 209
1571 99 244 217 1572 113 203 236 1573 152 214 229 1574 136 232 228
1575 13 236 232 1576 18 242 231 1577 14 239 232 1578 23 243 226
1579 15 236 227 1580 44 240 232 1581 51 239 225 1582 67 240 230
1583 105 235 228 1584 110 240 227 1585 118 236 201 1586 176 235 211
1587 199 237 220 1588 199 193 233 1589 213 201 234 1590 223 222 231
1591 221 113 236 1592 226 136 237 1593 231 158 228 1594 221 203 220
1595 229 224 224 1596 214 240 109 1597 221 243 134 1598 232 235 163
1599 236 234 234 1600 238 234 237 1601 228 246 40 1602 238 242 33
1603 236 240 42
1604 229 239 54 1605 238 238 59 1606 234 211 170 1607 238 218 182
1608 241 226 185 1609 233 109 226 1610 236 134 233 1611 229 158 238
1612 234 22 235 1613 234 8 233 1614 236 44 229 1615 237 54 229 1616
236 50 236 1617 235 96 238 1618 236 78 236 1619 237 124 239 1620
237 132 239 1621 237 125 237 1622 234 189 219 1623 237 204 222 1624
239 209 228 1625 234 244 147 1626 235 246 135 1627 237 243 159 1628
235 242 170 1629 235 239 178 1630 221 242 196 1631 226 243 200 1632
233 227 220 1633 237 235 235 1634 238 235 237 1635 219 181 233 1636
224 194 234 1637 227 207 231 1638 202 241 226 1639 176 238 232 1640
191 237 229 1641 222 228 225 1642 223 240 214 1643 216 239 215 1644
224 220 231 1645 224 241 225 1646 229 218 231 1647 228 235 211 1648
232 238 195 1649 236 238 200 1650 235 241 202 1651 240 214 223 1652
240 212 227 1653 234 169 236 1654 237 155 234 1655 236 178 237 1656
239 189 238 1657 239 193 236 1658 233 225 236 1659 239 234 224 1660
240 234 208 1661 234 236 230 1662 235 239 213 1663 236 240 212 1664
240 237 211 1665 235 241 211 1666 239 214 227 1667 238 235 237 1668
238 235 237 1669 236 238 212 1670 240 236 212 1671 235 238 220 1672
236 213 236 1673 231 237 230 1674 223 240 228 1675 232 240 220 1676
234 222 234 ______________________________________
______________________________________ APPENDIX F Q60.rgb: Q60, RGB
scan data Patch # R G B ______________________________________ 1 95
83 167 2 192 82 163 3 191 67 113 4 185 61 77 5 179 60 42 6 198 119
42 7 183 184 50 8 93 150 43 9 53 130 69 10 54 144 118 11 58 163 195
12 59 96 169 13 104 89 173 14 167 73 147 15 182 66 110 16 182 59 81
17 185 67 54 18 136 96 34 19 118 136 36 20 87 144 38 21 48 124 58
22 43 126 96 23 41 119 140 24 69 104 181 25 106 87 152 26 133 75
122 27 150 70 110 28 148 70 81 29 153 77 64 30 127 91 45 31 125 127
55 32 98 141 67 33 58 122 71 34 55 121 98 35 64 118 129 36 88 108
164 37 99 88 112 38 112 83 104 39 122 81 96 40 118 80 83 41 124 93
81 42 116 99 75 43 129 125 87 44 108 131 91 45 79 112 83 46 75 113
98 47 81 113 119 48 98 105 128 49 152 122 197 50 188 116 174 51 211
110 146 52 213 109 125 53 214 117 105 54 200 138 92 55 181 187 56
56 130 182 81 57 97 178 117 58 80 173 142 59 75 180 210 60 134 152
209 61 152 129 189 62 182 120 159 63 197 114 138 64 195 113 124 65
199 125 117 66 189 146 115 67 189 186 96 68 142 185 109 69 110 175
118 70 96 173 143 71 97 173 194 72 142 151 193 73 147 131 160 74
161 125 148 75 171 123 136 76 169 122 127 77 176 134 124 78 177 153
125 79 193 185 142 80 159 178 132 81 127 166 133 82 116 162 142 83
122 159 168 84 147 150 170 85 194 172 218 86 226 170 203 87 230 166
187 88 230 167 170 89 229 165 150 90 230 175 138 91 220 214 118 92
184 215 144 93 147 209 163 94 129 208 187 95 137 209 229 96 172 181
222 97 195 175 216 98 210 171 204 99 215 169 188 100 217 166 172
101 216 167 154 102 218 180 153 103 224 215 136 104 197 221 164 105
163 213 177 106 148 213 196 107 154 212 226 108 179 186 219 109 192
183 212 110 201 178 200 111 205 177 189 112 206 174 181 113 204 177
171 114 208 192 176 115 221 220 180 116 208 224 187 117 179 212 190
118 172 215 205 119 178 213 222 120 188 191 218 121 232 239 236 122
224 238 238 123 202 236 238 124 185 232 237 125 168 229 236 126 154
225 234 127 143 220 231 128 129 215 229 129 117 210 227 130 107 205
224 131 96 198 221 132 80 183 211 133 232 239 235 134 235 227 235
135 233 197 228 136 232 183 224 137 230 169 219 138 228 156 215 139
226 144 208 140 223 131 202 141 217 111 187 142 213 102 181 143 207
91 170 144 205 90 169 145 233 239 236 146 235 238 224 147 236 236
205 148 237 233 185 149 236 227 164 150 238 226 147 151 236 223 132
152 235 218 118 153 234 215 104 154 233 211 88 155 230 206 76 156
222 194 56 157 232 238 235 158 226 227 222 159 207 203 202 160 190
183 182 161 169 161 161 162 149 144 145 163 134 126 124 164 114 108
105 165 99 93 87 166 86 78 72 167 73 62 52 168 59 48 43 169 233 239
236 170 235 226 224 171 234 195 194 172 231 175 171 173 227 161 149
174 225 145 134 175 222 129 117 176 217 114 101 177 212 100 88 178
205 89 75 179 197 74 63 180 176 57 44 181 232 239 237 182 224 236
224 183 206 230 204 184 188 222 182 185 171 213 163 186 158 207 143
187 140 197 126 188 125 188 109 189 110 176 93 190 99 166 80 191 86
152 66 192 65 122 48 193 230 237 234 194 224 227 234 195 205 203
228 196 185 184 223 197 167 165 216 198 149 150 210 199 131 134 203
200 112 120 195 201 97 108 187 202 85 99 180 203 72 85 165 204 59
68 140 205 141 112 98 206 175 139 118 207 207 168 143 208 233 191
165 209 146 108 98 210 181 135 121 211 212 165 149 212 234 200 180
213 166 111 102 214 196 147 136 215 213 162 153 216 234 187 177 217
234 240 237 218 232 232 230 219 223 220 216 220 206 200 198 221 198
193 194 222 187 181 182 223 175 170 172 224 165 158 159 225 152 147
148 226 142 136 136 227 130 125 126 228 121 115 116 229 111 107 108
230 101 96 97 231 90 87 87 232 81 77 76 233 70 68 68 234 58 55 55
235 47 44 44 236 33 31 32
______________________________________
* * * * *